23.2.147 problem 150

Internal problem ID [5502]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 150
Date solved : Tuesday, September 30, 2025 at 12:45:40 PM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.057 (sec). Leaf size: 78

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

\[ y-\operatorname {RootOf}\left (-a \,\operatorname {arcsinh}\left (\frac {\operatorname {RootOf}\left (-2 a y+a^{2}+x^{2}+2 \textit {\_Z} a +\textit {\_Z}^{2}\right )}{x}\right )-x \sqrt {\frac {a \left (-2 \operatorname {RootOf}\left (-2 a y+a^{2}+x^{2}+2 \textit {\_Z} a +\textit {\_Z}^{2}\right )+2 \textit {\_Z} -a \right )}{x^{2}}}+c_1 \right ) = 0 \]

✓ Mathematica. Time used: 0.453 (sec). Leaf size: 70

ode=x^2 (D[y[x],x])^2+2 a x D[y[x],x]+a^2+x^2-2 a y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\left \{y(x)=\frac {2 a x K[1]+x^2 K[1]^2+a^2+x^2}{2 a},x=-\frac {a \text {arcsinh}(K[1])}{\sqrt {K[1]^2+1}}+\frac {c_1}{\sqrt {K[1]^2+1}}\right \},\{y(x),K[1]\}\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a**2 + 2*a*x*Derivative(y(x), x) - 2*a*y(x) + x**2*Derivative(y(x), x)**2 + x**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out