77.1.76 problem 95 (page 135)

Internal problem ID [17966]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 95 (page 135)
Date solved : Tuesday, January 28, 2025 at 11:18:43 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.167 (sec). Leaf size: 24

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

\begin{align*} y &= 2 x \\ y &= 0 \\ y &= \frac {\left (x +c_{1} \right )^{2}}{2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.279 (sec). Leaf size: 75

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

\begin{align*} y(x)\to x \left (2 \cosh (-\log (x)+c_1)-\sqrt {3} \sinh (-\log (x)+c_1)+1\right ) \\ y(x)\to x \left (2 \cosh (\log (x)+c_1)-\sqrt {3} \sinh (\log (x)+c_1)+1\right ) \\ y(x)\to 0 \\ y(x)\to 2 x \\ \end{align*}