ISI2016-DCG-67

Question

The general solution of the differential equation $2y{y}'-x=0$ is (assuming $C$ as an arbitrary constant of integration)

• A. $x^{2}-y^{2}=C$
• B. $2x^{2}-y^{2}=C$
• C. $2y^{2}-x^{2}=C$
• D. $x^{2}+y^{2}=C$

Answer 1

Rearranging the terms of the differential equation,  $2y\frac{dy}{dx}=x$. Now integrating on both sides,

$\Rightarrow$  $\int 2ydy=\int xdx$    $\Rightarrow$   $2\times (\frac{y^{2}}{2})= \frac{x^{2}}{2} +k$  i.e. $2y^{2}-x^{2}=C$

Option C is the answer.

Comments

Your answer is wrong .

Option C is correct . Integration of x will be $x^2/2$

Correct answer is $2y^2-x^2=C$

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Corrected my mistake. Thank you for pointing out