- #1
member 428835
Hi PF!
Can any of you help me reduce this ODE to find a solution?
$$y y''+2y'^2+xy'+\frac{1}{2}y = 0 \implies \\ (y y')'+y'^2+xy'+\frac{1}{2}y = 0 \implies\\ (yy')'+(xy)'+y'^2-\frac{1}{2}y=0$$
but here I am stopped. Am I even going the correct route? I know I can re-write this equation as terms primed, because a quadratic solves this ODE. Any help is awesome!
Can any of you help me reduce this ODE to find a solution?
$$y y''+2y'^2+xy'+\frac{1}{2}y = 0 \implies \\ (y y')'+y'^2+xy'+\frac{1}{2}y = 0 \implies\\ (yy')'+(xy)'+y'^2-\frac{1}{2}y=0$$
but here I am stopped. Am I even going the correct route? I know I can re-write this equation as terms primed, because a quadratic solves this ODE. Any help is awesome!