60.1.421 problem 432

Internal problem ID [10435]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 432
Date solved : Sunday, March 30, 2025 at 04:41:58 PM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.054 (sec). Leaf size: 78

ode:=(x*diff(y(x),x)+a)^2-2*a*y(x)+x^2 = 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: 0.74 (sec). Leaf size: 70

ode=x^2 - 2*a*y[x] + (a + x*D[y[x],x])^2==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(-2*a*y(x) + x**2 + (a + x*Derivative(y(x), x))**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out