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The solution of the differential equatio...

The solution of the differential equation
`(dy)/(dx) = e^(3x-2y) +x^(2)e^(-2y)`,is

A

`e^(2y)=e^(3x)+x^(3)+c`

B

`e^(2y)=e^(3x)-x^(3)+c`

C

`(e^(2y))/(2)=(1)/(3)(e^(3x-x3))+c`

D

`(e^(2y))/(2)=(1)/(3)(e^(3x+x3))+c`

Text Solution

Verified by Experts

The correct Answer is:
D
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as Solution of the differential equation (dy)/(dx)=e^(3x-2y)+x^2e^(-2y) is (e^(2y))/(2)=(e^(3x))/(3)+(x^2)/(2)+C Reason (R) : (dy)/(dx)=e^(3x-2y)+x^2e^(-2y) (dy)/(dx)=e^(-2y)(e^(3x)+x^2) separating the variables e^(2y)dy=(e^(3x)+x^2)dx int e^(2y)dy=int(e^(3x)+x^2)dx (e^(2y))/(2)=(e^(3x))/(3)+(x^3)/(3)+C .

NIKITA PUBLICATION-APPLICATION OF DEFINITE INTEGRAL-MULTIPLE CHOICE QUESTIONS:(MCQ)
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  17. The area of the plane region bounded by the curves x + 2y^(2)=0 and x+...

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  19. Find the area enclosed between the circle x ^ 2 + y ^ 2 = 1...

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