The solution of the differential equatio

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Differential Equations

Question:

The solution of the differential equation $x\frac{dy}{dx}+2y=x^2$ is : (C is constant of integration )

Options:

$x^2y=\frac{x^4}{4}+C$

$2xy=\frac{2}{3}x^3+C$

$x^2y=\frac{x^3}{3}+C$

$xy =\frac{x^4}{4}+C$

Correct Answer:

$x^2y=\frac{x^4}{4}+C$

Explanation:

$x\frac{dy}{dx}+2y=x^2$ so $\frac{dy}{dx}+\frac{2}{x}y=x$ ...(1)

so $I.F. = e^{\int\frac{2}{x}dx}=e^{ln|x^2|=x^2}$

Eqn. (1)

$⇒x^2\frac{dy}{dx}+2xy=x^3$ Integrating wrt x

$x^2y=\frac{x^4}{4}+C$