The differential equation $x \frac{d y}{

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Differential Equations

Question:

The differential equation $x \frac{d y}{d x}-y=x^2$, has the general solution

Options:

$y-x^3=2 C x$

$y-x^2=Cx$

$2 y+x^2=2 C x$

$y+x^2=2 C x$

Correct Answer:

$y-x^2=Cx$

Explanation:

$\frac{xd y}{d x}-y=x^2$

so $\frac{xdy-ydx}{x^2}=dx$

so $\int d(\frac{y}{x})=\int dx$

so $\frac{y}{x}=x+C$

so $y=x^2+Cx$

so $y-x^2=Cx$