Explore topic-wise MCQs in Ordinary Differential Equations.

This section includes 9 Mcqs, each offering curated multiple-choice questions to sharpen your Ordinary Differential Equations knowledge and support exam preparation. Choose a topic below to get started.

1.

Find the P.I for the given Differential Equation.
(16x^2 frac{d^2 y}{dx^2}+(2x+4) frac{dy}{dx}+4x(x+4) frac{d^2 y}{dx^2}+2y=cos (log (2x+4)) )

A. ( frac{1}{4} (-sin u2061(log u2061(2x+4))+cos u2061(log u2061(2x+4))) )
B. ( frac{1}{4} (-sin u2061(log u2061(2x+4))-cos u2061(log u2061(2x+4))) )
C. ( frac{1}{2} (-sin u2061(log u2061(2x+4))-cos u2061(log u2061(2x+4))) )
D. ( frac{1}{2} (-sin u2061(log u2061(2x+4))+cos u2061(log u2061(2x+4))) )
Answer» C. ( frac{1}{2} (-sin u2061(log u2061(2x+4))-cos u2061(log u2061(2x+4))) )
Discussion
2.

Find the C.F for the given Higher Order Differential Equation.
(x^2 frac{d^2 y}{dx^2}+3(x+2) frac{dy}{dx}+4(1+x) frac{d^2 y}{dx^2}+2y=x )

A. ( frac{1}{(x+1)} (c_1cos u2061(log u2061(x+2))+c_2sin u2061(log u2061(x+2))) )
B. ( frac{1}{(x+2)} (c_1cos u2061(log u2061(x+2))+c_2cos u2061(log u2061(x+2))) )
C. ( frac{1}{(x+1)} (c_1cos u2061(log u2061(x+1))+c_2sin u2061(log u2061(x+1))) )
D. ( frac{1}{(x+2)} (c_1cos u2061(log u2061(x+2))+c_2sin u2061(log u2061(x+2))) )
Answer» E.
Discussion
3.

Find the solution for the given Higher Order Differential Equation.
(2(3x+5)^2 frac{d^2 y}{dx^2}+(3x+5) frac{dy}{dx}+y=sin (log (3x+5)) )

A. (c_1(3x+5)^{0.76}+ c_2(3x+5)^{0.073}+ frac{-(15(cos u2061(log u2061(3x+5))+17 sin u2061(log u2061(3x+5)))))}{64} )
B. (c_1(3x+5)^{0.76}+ c_2(3x+7)^{0.073}+ frac{-(15(cos u2061(log u2061(3x+5))+17 sin u2061(log u2061(3x+5)))))}{64} )
C. (c_1(3x+5)^{0.76}+ c_2(3x+7)^{0.073}+ frac{-(15(cos u2061(log u2061(3x+5))+17 sin u2061(log u2061(3x+5)))))}{16} )
D. (c_1(3x+5)^{0.76}+ c_2(3x+5)^{0.073}+ frac{-(15(cos u2061(log u2061(3x+5))+17 sin u2061(log u2061(3x+5)))))}{16} )
Answer» B. (c_1(3x+5)^{0.76}+ c_2(3x+7)^{0.073}+ frac{-(15(cos u2061(log u2061(3x+5))+17 sin u2061(log u2061(3x+5)))))}{64} )
Discussion
4.

Find the C.F for the following Differential Equation.
((3x+2)^3 frac{d^3y}{dx^3}+2(3x+2)^2 frac{d^2 y}{dx^2}+(3x+2) frac{dy}{dx}-y=(3x+2)^2 )

A. (c_1(3x+2)^{0.022}+(3x+2)^{1.15}(c_2 cos u2061(0.22 log u2061(3x+2))+c_3 sin(0.22 log u2061(3x+2))) )
B. (c_1(3x+2)^{0.022}+(3x+2)^{1.15}(c_2 cos u2061(0.22 log u2061(3x+3))+c_3 sin(0.22 log u2061(3x+2))) )
C. (c_1(3x+2)^{0.026}+(3x+2)^{1.15}(c_2 cos u2061(0.22 log u2061(3x+2))+c_3 sin(0.22 log u2061(3x+2))) )
D. (c_1(3x+2)^{0.022}+(3x+2)^{1.15}(c_2 sin u2061(0.22 log u2061(3x+2))+c_3 sin(0.22 log u2061(3x+2))) )
Answer» D. (c_1(3x+2)^{0.022}+(3x+2)^{1.15}(c_2 sin u2061(0.22 log u2061(3x+2))+c_3 sin(0.22 log u2061(3x+2))) )
Discussion
5.

Solve this Differential Equation to find its General Solution.
((x+3) frac{d^2y}{dx^2}+2 frac{dy}{dx}+ frac{y}{(x+3)}=4 )

A. ( frac{4x}{3}+2+ frac{1}{(x+3)} c_1cos u2061( frac{ sqrt{3}}{2} log u2061(x+3))+c_2sin u2061( frac{ sqrt{3}}{2} log u2061(x+3)) )
B. ( frac{4x}{3}+4+ frac{1}{(x+3)} c_1cos u2061( frac{ sqrt{3}}{2} log u2061(x+3))+c_2sin u2061( frac{ sqrt{3}}{2} log u2061(x+3)) )
C. (x+4+ frac{1}{(x+3)} c_1cos u2061( frac{ sqrt{3}}{2} log u2061(x+3))+c_2sin u2061( frac{ sqrt{3}}{2} log u2061(x+3)) )
D. ( frac{2x}{3}+4+ frac{1}{(x+3)} c_1cos u2061( frac{ sqrt{3}}{2} log u2061(x+3))+c_2sin u2061( frac{ sqrt{3}}{2} log u2061(x+3)) )
Answer» C. (x+4+ frac{1}{(x+3)} c_1cos u2061( frac{ sqrt{3}}{2} log u2061(x+3))+c_2sin u2061( frac{ sqrt{3}}{2} log u2061(x+3)) )
Discussion
6.

Find the P.I of the given Differential Equation.
((x+1)^2 frac{d^2 y}{dx^2}+(x+1) frac{dy}{dx}+y=sin (log (1+x)) )

A. -log u2061(x+1) ( frac{cos u2061(log u2061(x+1))}{2} )
B. -log u2061(x+1) ( frac{sin u2061(log u2061(x+1))}{2} )
C. log u2061(x+1) ( frac{cos u2061(log u2061(x+1))}{2} )
D. -log u2061(x+2) ( frac{cos u2061(log u2061(x+1))}{2} )
Answer» B. -log u2061(x+1) ( frac{sin u2061(log u2061(x+1))}{2} )
Discussion
7.

Find the C.F of the following Differential Equation.
((2x+3)^2 frac{d^2 y}{dx^2} + (2x+3) frac{dy}{dx} 2y = x )

A. (c_1(2x+3)+ c_2(2x+3)^ frac{-1}{2} )
B. (c_1(2x+3)+ c_2(2x+3)^ frac{1}{2} )
C. (c_1(2x+3)+ c_2(2x+3)^ frac{-3}{2} )
D. (c_1(2x+3)+ c_2(2x+3)^ frac{-1}{2} )
Answer» B. (c_1(2x+3)+ c_2(2x+3)^ frac{1}{2} )
Discussion
8.

Find the Continuous Function and Particular Integral for the given differential equation.
((2x+3) frac{dy}{dx}-3y=8x )

A. (c_1(2x+3)^ frac{5}{2}, -4(2x+3)-4 )
B. (c_1(2x+3)^ frac{3}{2}, -2(2x+3)-4 )
C. (c_1(2x+3)^ frac{3}{2}, -4(2x+3)-4 )
D. (c_1(2x+3)^ frac{3}{2}, -4(2x+3)-4 )
Answer» D. (c_1(2x+3)^ frac{3}{2}, -4(2x+3)-4 )
Discussion
9.

Find the General Solution of the given differential equation.
((8x+7) frac{dy}{dx}+2y=x )

A. (c_1( frac{1}{(8x+7)})^ frac{1}{4}+ frac{(8x+7)}{40}- frac{5}{16} )
B. (c_1( frac{1}{(8x+7)})^ frac{1}{4}+ frac{(8x+7)}{80}- frac{7}{8} )
C. (c_1( frac{1}{(8x+7)})^ frac{1}{4}+ frac{(8x+7)}{40}- frac{7}{16} )
D. (c_1( frac{1}{(8x+7)})^ frac{1}{4}+ frac{(8x+7)}{80}- frac{7}{16} )
Answer» E.
Discussion