Internal problem ID [3651]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 924.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {4 x^{2} \left (y^{\prime }\right )^{2}-4 y y^{\prime } x -8 x^{3}+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.188 (sec). Leaf size: 30
dsolve(4*x^2*diff(y(x),x)^2-4*x*y(x)*diff(y(x),x) = 8*x^3-y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (-x \sqrt {2}+c_{1}\right ) \sqrt {x} \\ y \relax (x ) = \left (x \sqrt {2}+c_{1}\right ) \sqrt {x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.079 (sec). Leaf size: 42
DSolve[4 x^2 (y'[x])^2-4 x y[x] y'[x]==8 x^3 -y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {x} \left (-\sqrt {2} x+c_1\right ) \\ y(x)\to \sqrt {x} \left (\sqrt {2} x+c_1\right ) \\ \end{align*}