29.28.15 problem 813

Internal problem ID [5396]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 28
Problem number : 813
Date solved : Monday, January 27, 2025 at 11:18:50 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-2 \left (x -y\right ) y^{\prime }-4 y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

dsolve(diff(y(x),x)^2-2*(x-y(x))*diff(y(x),x)-4*x*y(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 28

DSolve[(D[y[x],x])^2-2*(x-y[x])*D[y[x],x]-4*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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