Internal problem ID [3632]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 904.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}+x \left (x^{3}-2 y\right ) y^{\prime }-\left (2 x^{3}-y\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.118 (sec). Leaf size: 109
dsolve(x^2*diff(y(x),x)^2+x*(x^3-2*y(x))*diff(y(x),x)-(2*x^3-y(x))*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {x^{3}}{4} \\ y \relax (x ) = -\frac {x^{3}}{2}+c_{1}^{2} x -\frac {\left (-x -2 c_{1}\right ) x^{2}}{2} \\ y \relax (x ) = -\frac {x^{3}}{2}+c_{1}^{2} x -\frac {\left (-x +2 c_{1}\right ) x^{2}}{2} \\ y \relax (x ) = -\frac {x^{3}}{2}+c_{1}^{2} x +\frac {\left (x -2 c_{1}\right ) x^{2}}{2} \\ y \relax (x ) = -\frac {x^{3}}{2}+c_{1}^{2} x +\frac {\left (x +2 c_{1}\right ) x^{2}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.855 (sec). Leaf size: 48
DSolve[x^2 (y'[x])^2+x(x^3-2 y[x])y'[x]-(2 x^3-y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{c_1} x \left (e^{c_1}-i x\right ) \\ y(x)\to -e^{c_1} x \left (i x+e^{c_1}\right ) \\ y(x)\to 0 \\ \end{align*}