$y=ex-c^{2}$ is the solution of the di

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Differential Equations

Question:

$y=ex-c^{2}$ is the solution of the differential equation

Options:

$\left(\frac{dy}{dx}\right)^{2}+x\left(\frac{dy}{dx}\right)+y=0$

$\frac{d^{2}y}{dx^{2}}=0$

$\frac{dy}{dx}=0$

$\left(\frac{dy}{dx}\right)^{2}-x\left(\frac{dy}{dx}\right)+y=0$

Correct Answer:

$\left(\frac{dy}{dx}\right)^{2}-x\left(\frac{dy}{dx}\right)+y=0$

Explanation:

Check that $y=ex-c^{2}$ satisfies the equation given in (d). $\frac{dy}{dx}=c\hspace{1cm}$ So, $\left(\frac{dy}{dx}\right)^{2}-x\left(\frac{dy}{dx}\right)+y=c^{2}-xc+cx-x^{2}=0$

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