Question

The solution of the differential equation $y_1 y_3=3 y_2^2$ is

• A. $x=A_1 y^2+A_2 y+A_3$
• B. $x=A_1 y+A_2$
• C. $x=A_1 y^2+A_2 y$
• D. $y=A_1 x+A_2$

Answer 1

Answer: (A)

$y_1 y_3=3 y_2^2$
$\frac{y_3}{y_2}=3 \frac{y_2}{y_1} \Rightarrow \ell n y_2 = 3\ell ny_1 + \ell n c$
$y_2=c y_1{ }^3$
$\frac{y_2}{y_1^2}=c y_1$
$-\frac{1}{y_1}=c y+c_2$
$\frac{d x}{d y}=-c y-c_2$
$x=-\frac{c y_2}{2}-c_2 y+c_3$
$\therefore x=A_1 y_1+A_2 y+A_3$