Internal problem ID [8025]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 445.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}+\left (a \,x^{2} y^{3}+b \right ) y^{\prime }+y^{3} a b=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(x^2*diff(y(x),x)^2+(a*x^2*y(x)^3+b)*diff(y(x),x)+a*b*y(x)^3 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {b}{x}+c_{1} \\ y \relax (x ) = \frac {1}{\sqrt {2 x a +c_{1}}} \\ y \relax (x ) = -\frac {1}{\sqrt {2 x a +c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 49
DSolve[a*b*y[x]^3 + (b + a*x^2*y[x]^3)*y'[x] + x^2*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {2 a x-2 c_1}} \\ y(x)\to \frac {1}{\sqrt {2 a x-2 c_1}} \\ y(x)\to \frac {b}{x}+c_1 \\ \end{align*}