77.1.93 problem 120 (page 179)

Internal problem ID [17983]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 120 (page 179)
Date solved : Tuesday, January 28, 2025 at 11:19:25 AM
CAS classification : [NONE]

\begin{align*} x \left (x^{2} y^{\prime }+2 y x \right ) y^{\prime \prime }+4 x {y^{\prime }}^{2}+8 x y y^{\prime }+4 y^{2}-1&=0 \end{align*}

✗ Solution by Maple

dsolve(x*(x^2*diff(y(x),x)+2*x*y(x))*diff(y(x),x$2)+4*x* diff(y(x),x)^2 + 8*x*y(x)*diff(y(x),x) + 4*y(x)^2-1=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[x*(x^2*D[y[x],x]+2*x*y[x])*D[y[x],{x,2}]+4*x* D[y[x],x]^2 + 8*x*y[x]*D[y[x],x]+ 4*y[x]^2-1==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved