60.1.421 problem 423

Internal problem ID [10435]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 423
Date solved : Monday, January 27, 2025 at 07:43:46 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.075 (sec). Leaf size: 44

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

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

✓ Solution by Mathematica

Time used: 0.182 (sec). Leaf size: 78

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