29.35.18 problem 1051

Internal problem ID [5616]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 35
Problem number : 1051
Date solved : Monday, January 27, 2025 at 12:26:55 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+x y \left (x^{2}+y x +y^{2}\right ) y^{\prime }-x^{3} y^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 32

dsolve(diff(y(x),x)^3-(x^2+x*y(x)+y(x)^2)*diff(y(x),x)^2+x*y(x)*(x^2+x*y(x)+y(x)^2)*diff(y(x),x)-x^3*y(x)^3 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {x^{3}}{3}+c_{1} \\ y \left (x \right ) &= \frac {1}{-x +c_{1}} \\ y \left (x \right ) &= {\mathrm e}^{\frac {x^{2}}{2}} c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.106 (sec). Leaf size: 48

DSolve[(D[y[x],x])^3 -(x^2+x y[x]+ y[x]^2) (D[y[x],x])^2 +x y[x](x^2 +x y[x]+ y[x]^2) D[y[x],x]-x^3 y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{x+c_1} \\ y(x)\to c_1 e^{\frac {x^2}{2}} \\ y(x)\to \frac {x^3}{3}+c_1 \\ y(x)\to 0 \\ \end{align*}