Internal problem ID [15093]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 8. First order not solved for the derivative. Exercises page 67
Problem number: 205.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{3}-y {y^{\prime }}^{2}+x^{2} y^{\prime }-x^{2} y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve(diff(y(x),x)^3=y(x)*diff(y(x),x)^2-x^2*diff(y(x),x)+x^2*y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {i x^{2}}{2}+c_{1} \\ y \left (x \right ) &= \frac {i x^{2}}{2}+c_{1} \\ y \left (x \right ) &= {\mathrm e}^{x} c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 43
DSolve[y'[x]^3==y[x]*y'[x]^2-x^2*y'[x]+x^2*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^x \\ y(x)\to c_1-\frac {i x^2}{2} \\ y(x)\to \frac {i x^2}{2}+c_1 \\ \end{align*}