29.28.23 problem 821

Internal problem ID [5404]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 28
Problem number : 821
Date solved : Monday, January 27, 2025 at 11:20:59 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-\left (1+2 y x \right ) y^{\prime }+2 y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 16

dsolve(diff(y(x),x)^2-(1+2*x*y(x))*diff(y(x),x)+2*x*y(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 21

DSolve[(D[y[x],x])^2-(1+2*x*y[x])*D[y[x],x]+2*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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