29.30.9 problem 868

Internal problem ID [5449]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 868
Date solved : Monday, January 27, 2025 at 11:24:14 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.087 (sec). Leaf size: 44

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

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

✓ Solution by Mathematica

Time used: 0.221 (sec). Leaf size: 78

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

\begin{align*} y(x)\to -\frac {1}{2} e^{-c_1} x^2+x-e^{c_1} \\ y(x)\to -e^{c_1} x^2+x-\frac {e^{-c_1}}{2} \\ y(x)\to x-\sqrt {2} x \\ y(x)\to \left (1+\sqrt {2}\right ) x \\ \end{align*}