60.1.419 problem 421

Internal problem ID [10433]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 421
Date solved : Monday, January 27, 2025 at 07:43:42 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.068 (sec). Leaf size: 30

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

\begin{align*} y &= -i x \\ y &= i x \\ y &= \frac {-c_{1}^{2}+x^{2}}{2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.082 (sec). Leaf size: 45

DSolve[-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 x \sinh (-\log (x)+c_1) \\ y(x)\to x \sinh (\log (x)+c_1) \\ y(x)\to -i x \\ y(x)\to i x \\ \end{align*}