60.1.384 problem 385

Internal problem ID [10398]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 385
Date solved : Monday, January 27, 2025 at 07:39:03 PM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Solution by Maple

Time used: 0.047 (sec). Leaf size: 161

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

\begin{align*} y &= \frac {x^{4}-\operatorname {RootOf}\left (x^{16}-12 \textit {\_Z}^{2} x^{12}+16 \textit {\_Z}^{3} x^{10}+30 \textit {\_Z}^{4} x^{8}-96 \textit {\_Z}^{5} x^{6}+100 \textit {\_Z}^{6} x^{4}-48 \textit {\_Z}^{7} x^{2}+9 \textit {\_Z}^{8}-16 c_{1} x^{4}\right )^{2}}{2 x} \\ y &= \frac {x^{4}-\operatorname {RootOf}\left (x^{16}-12 \textit {\_Z}^{2} x^{12}-16 \textit {\_Z}^{3} x^{10}+30 \textit {\_Z}^{4} x^{8}+96 \textit {\_Z}^{5} x^{6}+100 \textit {\_Z}^{6} x^{4}+48 \textit {\_Z}^{7} x^{2}+9 \textit {\_Z}^{8}-16 c_{1} x^{4}\right )^{2}}{2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 60.483 (sec). Leaf size: 4749

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

Too large to display