Worksheets Class 12 Mathematics Differential Equations

Students should refer to Worksheets Class 12 Mathematics Differential Equations Chapter 9 provided below with important questions and answers. These important questions with solutions for Chapter 9 Differential Equations have been prepared by expert teachers for Class 12 Mathematics based on the expected pattern of questions in the class 12 exams. We have provided Worksheets for Class 12 Mathematics for all chapters on our website. You should carefully learn all the important examinations questions provided below as they will help you to get better marks in your class tests and exams.

Differential Equations Worksheets Class 12 Mathematics

Question. The solution of the differential equation cos²x d²y/dx² = 1 is:  
(a) y = log cos x + cx
(b) y = logsec x + c₁x + c₂
(c) y = logsec x − c₁x + c₂
(d) None of these

Question. The differential equation of system of concentric circles with centre (1,2) is

Question. The differential equation of all circles which pass through origin and whose centres lie on y-axis is

Question. The differential equation of the family of curves y2=4a (x +a) is

Question. The differential equation of the rectangular hyperbola whose axes are the asymptotes of the hyperbola, is
(a) ydy/dx= x
(b) xdy/dx= – y
(c) xdydx= y
(d) xdy+ y dx =C

Question. The differential equation by eliminating A and B in

Question. The equation of the curve through the point (1,1) and whose slope is 2ay/x(y-a), is

Question. The differential equation of the family of curves y²=4a (x +a) is 20

Question. The differential equation of all circles passing through the origin and having their centres on the x-axis is

Question. The differential equation of the family of parabolas with focus at the origin and the x-axis as axis, is

Question. A particular solution of the differential equation x-0, is

Question. The particular solution of the differential equation

Question. The differential equation that represents all parabolas each of which has a latusrectum 4a and whose axes are parallel to x-axis, is

Question. The particular solution of the differential equation

Question. The equation of a curve passing through the point (0, 0) and whose differential equation is y’= e^x  sin x is

Question. The equation of the curve passing through the point

Question. The particular solution of the differential equation

Question. Particular solution of the differential equation

Question. Solution of the differential equation

Question. If y(x) is a solution of (2+sin x /1+y)dy/dx=-cos x and y(0) =1,then the value of y(π/2) is
(a) 1/3
(b) 1/2
(c) 1
(d) 0

Question. If y (t) is a solution of (1+t)dy/dt-ty=1 and y (0)=-1,then the value of y(1) is 
(a) 1
(b) -1
(c) -1/2
(d) 0 C

Question.

Question.

Question. A continuously differential function Φ (x) in (0,π) satisfying y’=1+y2,y(0)=0=y(π), is 
(a) tan x
(b) x (x-π)
(c) (x-π)(1-e^x)
(d) Not possible 

Question. The differential equation d²y/dx²=2  represents 
(a) a parabola whose axis is parallel to x-axis
(b) a parabola whose axis is parallel to y-axis
(c) a circle
(d) None of the above

Question.

Question. The solution of dy/dx=x2+y2+1/2xy, satisfying y(1)=1,
is given by a
(a) hyperbola
(b) circle
(c) ellipse
(d) parabola 

Question. The general solution of differential equation

Question. Solution of the differential equation

Question. Solution of the differential equation

Question. Solution of the differential equation

Question. If d²y/dx² = 0,then:
(a) y = ax + b
b) y² = ax + b
(c) y = log x
(d) y = e^x + c

Question. The order of the differential equation, whose general solution is y= c₁e^x + c₂e^2x + c₃e^3x + c₄e^x+c3 , where c₁,c₂,c₃, c₄, c₅ are arbitrary constants is:
(a) 5
(b) 4
(c) 3
(d) 2

Question. The degree of the differential equation satisfying √1− x² + √1− y² = a(x − y) is:
(a) 1
(b) 2
(c) 3
(d) 4

Question. Family y = Ax + A³ of curve represented by the differential equation of degree:
(a) Three
(b) Two
(c) One
(d) None of these

Question. The second order differential equation is:
(a) y′² + x = y²
(b) y′y′′ + y = sin x
(c) y′′′ + y′′ + y = 0
(d) y′ = y

Question. The degree of differential equation d2y/dx2 +(dy/dx)3 + 6y =0 is:
(a) 1
(b) 3
(c) 2
(d) 5

Question. The solution of the differential equation xcos ydy = (xe logx + ex)dx is:
(a) sin y = 1/x e^x + c
(b) sin y + e^x logx + c = 0
(c) sin y = e^x logx + c 
(d) None of these 

Question. The solution of the differential equation dy/dx = sec x(sec x + tan x) is:
(a) y = sec x + tan x + c
(b) y = sec x + cot x + c
(c) y = sec x − tan x + c
(d) None of these

Question. The degree and order of the differential equation of the family of all parabolas whose axis is x–axis, are respectively:
(a) 2, 1
(b) 1, 2
(c) 3, 2
(d) 2, 3

Question. The order and degree of the differential equation x(dy/dx)3 + 2(d2y/dx2)3 + 3y +x = 0 are respectively:
(a) 3, 2
(b) 2, 1
(c) 2, 2
(d) 2, 3

Question. The order of differential equations of all parabolas having directrix parallel to x-axis is:
(a) 3
(b) 1
(c) 4
(d) 2

Question. The differential equation for the line y = mx + c is: (where c is arbitrary constant)
(a) dy/dx = m
(b) dy/dx + m
(c) dy/dx = 0
(d) None of these

Question. The differential equation found by the elimination of the arbitrary constant K from the equation y = (x+K)e−x is:
(a) dy/dx−y = e−x
(b) dy/dx−ye^x = 1
(c) dy/dx+ ye^x = 1
(d) dy/dx + y = e^−x

Question. The elimination of the arbitrary constants A, B and C from y = A + Bx Ce^−x leads to the differential equation:
(a) y′′′ − y′ = 0
(b) y′′′ − y′′ + y′ = 0
(c) y′′′ + y′′ = 0
(d) y′′ + y′′ − y′ = 0

Question. The solution of the differential equation dy/dx = (4x + y +1)² is:
(a) 4x – y + 1 = 2 tan (2x – 2c)
(b) 4x – y – 1 = 2 tan (2x – 2c)
(c) 4x + y + 1 = 2 tan (2x + 2c)
(d) None of these

Question. The order and degree of the differential equation

(a) 1, 2
(b) 2,1
(c) 1, 1
(d) 2,2

Question. The order and degree of the differential equation

(a) 2,3
(b) 3,3
(c) 2,6
(d) 2,4

Question. The solution of the differential equation 3ex tan ydx + (1–e^x )sec²ydy = 0 is:
(a) tan y = c(1−e^x)³
(b) (1−e^x)³ tan y = c
(c) tan y = c(1−e^x)
(d) (1−e^x) tan y = c

Question. The solution of the equation sin−1(dy/dx) = x+y is:
(a) tan(x + y) + sec(x + y) = x + c
(b) tan(x + y) − sec(x + y) = x + c
(c) tan(x + y) + sec(x + y) + x + c = 0
(d) None of these

Question. Solution of y(2xy + e^x )dx = e^xdy is:
(a) yx² + e^x = cy
(b) xy² + e^x = cx
(c) xy² + e^−x = c
(d) None of these

Question. Solution of differential equation x dy − y dx = 0 represents:
(a) Rectangular hyperbola
(b) Straight line passing through origin
(c) Parabola whose vertex is at origin
(d) Circle whose centre is at origin

Question. A particle starts at the origin and moves along the x–axis in such a way that its velocity at the point (x, 0) is given by the formula dy/dx = cos2πx . Then the particle never reaches the point on:
(a) x = 1/4
(b) x = 3/4
(c) x = 1/2
(d) x = 1

Question. The general solution of the differential equation (x + y) dx + xdy = 0 is:
(a) x² + y² = c
(b) 2x² − y² = c
(c) x² + 2xy = c
(d) y² + 2xy = c

Question. The solution of ydx − xdy + xdy + 3x²y²e^x3 dx = 0 is:
(a) x/y + ex3 = c
(b) x/y − ex3 = c
(c) −x/y + e^x3 = c
(d) None of these

Question. Solution of (xy cos xy + sin xy)dx + x² cos xy dy = 0 is:
(a) xsin(xy) = k
(b) xy sin(xy) = k
(c) x/y sin(xy)
(d) x sin(xy)+ xy cos xy = k

Question. If c is any arbitrary constant, then the general solution of the differential equation ydx − xdy = xy dx is given by:
(a) y = cx e^−x
(b) x = cye^−x
(c) y + e^x = cx
(d) ye^x = cx

Question. The equation of the curve which passes through the point (1, 1) and whose slope is given by 2y/x , is:
(a) y = x²
(b) x² − y² = 0
(c) 2x² + 2y² = 3
(d) None of these

Question. Equation of curve through point (1, 0)which satisfies the differential equation (1+ y²)dx − xydy = 0 , is:
(a) x² + y² = 0 =1
(b) x² − y² = 0 =1
(c) 2x² + y² = 0 = 2
(d) None of these

Question. The general solution of the differential equation (x + y)dx + xdy = 0 is:
(a) x² + y² = c
(b) 2x² – y² = c
(c) x² + 2xy = c
(d) y² + 2xy = c

Question. The general solution of the differential equation (2x − y +1) dx + (2y − x +1)dy = 0 is:
(a) x² + y² + xy − x + y = c
(b) x² + y² − xy + x + y = c
(c) x² + y² + 2xy − x + y = c
(d) x² + y² − 2xy + x − y = c

Question. The differential equation y dy/dx + x = a (a is any constant) represents:
(a) A set of circles having centre on the y-axis
(b) A set of circles centre on the x-axis
(c) A set of ellipses
(d) None of these

Question. The solution of the differential equation x d²y/dx² = 1 given that y = 1 , dy/dx when x =1, is:
(a) y = x log x + x + 2
(b) y = x log x − x + 2
(c) y = x log x + x
(d) y = x log x − x