Explore topic-wise MCQs in Ordinary Differential Equations.

This section includes 5 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.

Solution of the differential equation ( frac{dy}{dx} = frac{y-x+1}{y+x+5} ) is ______

A. ( -tan{-1} u2061 frac{y+3}{x+2} log sqrt{(x+2)^2+(y+3)^2}=c )
B. (-tan{-1} u2061 u2061 frac{y+3}{x+2} log sqrt{(x+2)^2+(y+3)^2}=c )
C. (tan{-1} u2061 u2061 frac{y+3}{x+2} log sqrt{x+y+5}=c )
D. (-cot{-1} u2061 u2061 frac{y+3}{x+2} log sqrt{x+y+5}=c )
Answer» C. (tan{-1} u2061 u2061 frac{y+3}{x+2} log sqrt{x+y+5}=c )
Discussion
2.

Solution of the differential equation ( frac{dy}{dx} = frac{x+2y-3}{2x+y-3} ) is _____

A. (x+y)=c(x-y)<sup>2</sup>
B. (x+y-2)=c(x-y)<sup>3</sup>
C. (2x+y)=c(x+2y)<sup>2</sup>
D. (2x+y-3)=c(x-2y-3)<sup>3</sup>
Answer» C. (2x+y)=c(x+2y)<sup>2</sup>
Discussion
3.

Solution of the differential equation (x-y)dy=(x+y+1)dx is _____

A. ( sqrt{x^2+y^2} = e^{c tan^{-1} u2061 left( frac{y+0.5}{x+0.5} right)} )
B. ((x^2+y^2)^1.5 = c cot^{-1} u2061 left( frac{y+0.5}{x+0.5} right) )
C. ((x^2+y^2)^2 = e^{c cot u2061 u2061 left( frac{y+0.5}{x+0.5} right)} )
D. ((x^2+y^2)^1 = c tan u2061 left( frac{y+0.5}{x+0.5} right) )
Answer» B. ((x^2+y^2)^1.5 = c cot^{-1} u2061 left( frac{y+0.5}{x+0.5} right) )
Discussion
4.

Solution of the differential equation (3y-7x+7)dx+(7y-3x+3)dy=0 is ______

A. p=(y+x)<sup>5</sup> (y-x)<sup>2</sup>
B. p=(y+x+2)<sup>5</sup> (y-x+2)<sup>2</sup>
C. p=(y+x)<sup>2</sup> (y-x)<sup>5</sup>
D. p=(y+x-1)<sup>5</sup> (y-x+1)<sup>2</sup>
Answer» E.
Discussion
5.

Solution of the differential equation ( frac{dy}{dx} = frac{3x-6y+7}{x-2y+4} ) is _____

A. log(x-2y+4)<sup>2</sup>=c
B. 6x-2y+log(x-2y+2)<sup>2</sup>=c
C. x-2y+log(x-2y+6)<sup>2</sup>=c
D. -5x+log(x-2y+3)<sup>2</sup>=c
Answer» C. x-2y+log(x-2y+6)<sup>2</sup>=c
Discussion