Mathematics - Differential Equation Question with Solution | TestHub

$y_1{y}_3=3y_2^2$

$\frac{y_3}{y_2}=3\frac{y_2}{y_1}\Rightarrow \ln y_2=3\ln y_1+\ln c$

$y_2=c{y}_1^3$

$\frac{y_2}{y_1^2}=c{y}_1$ $-\frac{1}{y_1}=cy+c_2$

$\frac{dx}{dy}=-cy-c_2$

$x=-\frac{c{y}^2}{2}-c_{2}y+c_3$

$\therefore x=A_1{y}^2+A_{2}y+A_3$