77.1.72 problem 91 (page 135)

Internal problem ID [17962]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 91 (page 135)
Date solved : Tuesday, January 28, 2025 at 11:18:35 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x {y^{\prime }}^{2}-2 y^{\prime } y+4 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.135 (sec). Leaf size: 30

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

\begin{align*} y &= -2 x \\ y &= 2 x \\ y &= \frac {4 c_{1}^{2}+x^{2}}{2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.286 (sec). Leaf size: 43

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

\begin{align*} y(x)\to -2 x \cosh (-\log (x)+c_1) \\ y(x)\to -2 x \cosh (\log (x)+c_1) \\ y(x)\to -2 x \\ y(x)\to 2 x \\ \end{align*}