Internal problem ID [4159]
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]
\[ \boxed {4 x^{2} {y^{\prime }}^{2}-4 y y^{\prime } x +y^{2}=8 x^{3}} \]
✓ Solution by Maple
Time used: 0.047 (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 \left (x \right ) = \left (-\sqrt {2}\, x +c_{1} \right ) \sqrt {x} y \left (x \right ) = \left (\sqrt {2}\, x +c_{1} \right ) \sqrt {x} \end{align*}
✓ Solution by Mathematica
Time used: 0.076 (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*}