Internal problem ID [4140]
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]
\[ \boxed {x^{2} {y^{\prime }}^{2}+x \left (x^{3}-2 y\right ) y^{\prime }-\left (2 x^{3}-y\right ) y=0} \]
✓ Solution by Maple
Time used: 0.047 (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 \left (x \right ) = -\frac {x^{3}}{4} y \left (x \right ) = -\frac {x^{3}}{2}+x \,c_{1}^{2}-\frac {\left (-x -2 c_{1} \right ) x^{2}}{2} y \left (x \right ) = -\frac {x^{3}}{2}+x \,c_{1}^{2}-\frac {\left (-x +2 c_{1} \right ) x^{2}}{2} y \left (x \right ) = -\frac {x^{3}}{2}+x \,c_{1}^{2}+\frac {\left (x -2 c_{1} \right ) x^{2}}{2} y \left (x \right ) = -\frac {x^{3}}{2}+x \,c_{1}^{2}+\frac {\left (x +2 c_{1} \right ) x^{2}}{2} \end{align*}
✓ Solution by Mathematica
Time used: 1.874 (sec). Leaf size: 58
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 -x (\cosh (c_1)+\sinh (c_1)) (-i x+\cosh (c_1)+\sinh (c_1)) y(x)\to -x (\cosh (c_1)+\sinh (c_1)) (i x+\cosh (c_1)+\sinh (c_1)) y(x)\to 0 \end{align*}