First slide

Types of solutions of differential equations

Question

$The solution of the differential y (xy + 2 x^{2} y^{2}) dx + x (xy - x^{2} y^{2}) dy = 0 is given by$

Moderate

A

$2log |x| -log |y| - \frac{1}{xy} =c$
B

$2log |y| -log |x| - \frac{1}{xy} =c$
C

$2log |x| +log |y| + \frac{1}{xy} =c$
D

$2log |y| +log |x| + \frac{1}{xy} =c$

Solution

${xy(ydx+xdy)+x}^{2} y^{2} (2ydx-xdy)=0$
$\begin{array}{l} \div b y x^{3} y^{3} \Rightarrow \int \frac{d (xy)}{x^{2} y^{2}} + \int (\frac{2}{x} dx - \frac{1}{y} dy) = \int 0 \\ \Rightarrow - \frac{1}{xy} + 2 \log | x | - \log | y | = c \end{array}$

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