75.8.7 problem 205

Internal problem ID [16823]
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
Date solved : Tuesday, January 28, 2025 at 09:33:56 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{3}&=y {y^{\prime }}^{2}-x^{2} y^{\prime }+x^{2} y \end{align*}

✓ Solution by Maple

Time used: 0.084 (sec). Leaf size: 28

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 &= -\frac {i x^{2}}{2}+c_{1} \\ y &= \frac {i x^{2}}{2}+c_{1} \\ y &= {\mathrm e}^{x} c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 43

DSolve[D[y[x],x]^3==y[x]*D[y[x],x]^2-x^2*D[y[x],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*}