54.1.264 problem 270

Internal problem ID [11578]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 270
Date solved : Tuesday, September 30, 2025 at 09:35:18 PM
CAS classification : [_exact, _rational]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 316

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

\begin{align*} y &= \frac {\left (-4 x^{3}-12 c_1 +4 \sqrt {x^{6}+\left (6 c_1 -4\right ) x^{3}+9 c_1^{2}}\right )^{{2}/{3}}+4 x}{2 \left (-4 x^{3}-12 c_1 +4 \sqrt {x^{6}+\left (6 c_1 -4\right ) x^{3}+9 c_1^{2}}\right )^{{1}/{3}}} \\ y &= \frac {i \left (-\left (-4 x^{3}-12 c_1 +4 \sqrt {x^{6}+\left (6 c_1 -4\right ) x^{3}+9 c_1^{2}}\right )^{{2}/{3}}+4 x \right ) \sqrt {3}-\left (-4 x^{3}-12 c_1 +4 \sqrt {x^{6}+\left (6 c_1 -4\right ) x^{3}+9 c_1^{2}}\right )^{{2}/{3}}-4 x}{4 \left (-4 x^{3}-12 c_1 +4 \sqrt {x^{6}+\left (6 c_1 -4\right ) x^{3}+9 c_1^{2}}\right )^{{1}/{3}}} \\ y &= \frac {i \left (\left (-4 x^{3}-12 c_1 +4 \sqrt {x^{6}+\left (6 c_1 -4\right ) x^{3}+9 c_1^{2}}\right )^{{2}/{3}}-4 x \right ) \sqrt {3}-\left (-4 x^{3}-12 c_1 +4 \sqrt {x^{6}+\left (6 c_1 -4\right ) x^{3}+9 c_1^{2}}\right )^{{2}/{3}}-4 x}{4 \left (-4 x^{3}-12 c_1 +4 \sqrt {x^{6}+\left (6 c_1 -4\right ) x^{3}+9 c_1^{2}}\right )^{{1}/{3}}} \\ \end{align*}

✓ Mathematica. Time used: 2.738 (sec). Leaf size: 326

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

\begin{align*} y(x)&\to -\frac {2 x+\sqrt [3]{2} \left (x^3+\sqrt {x^6+(-4+6 c_1) x^3+9 c_1{}^2}+3 c_1\right ){}^{2/3}}{2^{2/3} \sqrt [3]{x^3+\sqrt {x^6+(-4+6 c_1) x^3+9 c_1{}^2}+3 c_1}}\\ y(x)&\to \frac {2^{2/3} \left (1-i \sqrt {3}\right ) \left (x^3+\sqrt {x^6+(-4+6 c_1) x^3+9 c_1{}^2}+3 c_1\right ){}^{2/3}+\sqrt [3]{2} \left (2+2 i \sqrt {3}\right ) x}{4 \sqrt [3]{x^3+\sqrt {x^6+(-4+6 c_1) x^3+9 c_1{}^2}+3 c_1}}\\ y(x)&\to \frac {2^{2/3} \left (1+i \sqrt {3}\right ) \left (x^3+\sqrt {x^6+(-4+6 c_1) x^3+9 c_1{}^2}+3 c_1\right ){}^{2/3}+\sqrt [3]{2} \left (2-2 i \sqrt {3}\right ) x}{4 \sqrt [3]{x^3+\sqrt {x^6+(-4+6 c_1) x^3+9 c_1{}^2}+3 c_1}} \end{align*}

✗ Sympy

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

Timed Out