60.1.394 problem 396

Internal problem ID [10408]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 396
Date solved : Monday, January 27, 2025 at 07:40:29 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.138 (sec). Leaf size: 34

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