29.29.1 problem 823

Internal problem ID [5406]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 29
Problem number : 823
Date solved : Monday, January 27, 2025 at 11:21:06 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.140 (sec). Leaf size: 34

DSolve[(D[y[x],x])^2-(x-y[x])*y[x]*D[y[x],x]-x*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 0 \\ \end{align*}