Internal problem ID [3641]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 913.
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 +b y^{3} x^{2}\right ) y^{\prime }+a b y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 35
dsolve(x^2*diff(y(x),x)^2+(a+b*x^2*y(x)^3)*diff(y(x),x)+a*b*y(x)^3 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{\sqrt {2 b x +c_{1}}} \\ y \relax (x ) = -\frac {1}{\sqrt {2 b x +c_{1}}} \\ y \relax (x ) = \frac {a}{x}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 49
DSolve[x^2 (y'[x])^2+(a+b x^2 y[x]^3)y'[x]+a b y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {2 b x-2 c_1}} \\ y(x)\to \frac {1}{\sqrt {2 b x-2 c_1}} \\ y(x)\to \frac {a}{x}+c_1 \\ \end{align*}