29.32.18 problem 952

Internal problem ID [5530]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 32
Problem number : 952
Date solved : Monday, January 27, 2025 at 11:35:36 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 34

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

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

✓ Solution by Mathematica

Time used: 0.099 (sec). Leaf size: 54

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

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