77.1.49 problem 68 (page 109)

Internal problem ID [17939]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 68 (page 109)
Date solved : Tuesday, January 28, 2025 at 11:14:13 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.123 (sec). Leaf size: 31

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

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

✓ Solution by Mathematica

Time used: 0.142 (sec). Leaf size: 63

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

\begin{align*} y(x)\to e^{c_1}-2 e^{\frac {c_1}{2}} \sqrt {x} \\ y(x)\to 2 e^{-\frac {c_1}{2}} \sqrt {x}+e^{-c_1} \\ y(x)\to 0 \\ y(x)\to -x \\ \end{align*}