60.1.284 problem 290

Internal problem ID [10298]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 290
Date solved : Wednesday, March 05, 2025 at 10:02:29 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _dAlembert]

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

✓ Maple. Time used: 0.058 (sec). Leaf size: 1113

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 60.388 (sec). Leaf size: 744

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

\begin{align*} y(x)\to \frac {2^{2/3} \sqrt [3]{\sqrt {-4 x^6 \left (b^2-a c\right )^3+\left (a^2 \left (-d x^3+e^{3 c_1}\right )+3 a b c x^3-2 b^3 x^3\right ){}^2}-a^2 d x^3+a^2 e^{3 c_1}+3 a b c x^3-2 b^3 x^3}+\frac {2 \sqrt [3]{2} x^2 \left (b^2-a c\right )}{\sqrt [3]{\sqrt {-4 x^6 \left (b^2-a c\right )^3+\left (a^2 \left (-d x^3+e^{3 c_1}\right )+3 a b c x^3-2 b^3 x^3\right ){}^2}-a^2 d x^3+a^2 e^{3 c_1}+3 a b c x^3-2 b^3 x^3}}-2 b x}{2 a} \\ y(x)\to \frac {9 i 2^{2/3} \left (\sqrt {3}+i\right ) \sqrt [3]{\sqrt {-4 x^6 \left (b^2-a c\right )^3+\left (a^2 \left (-d x^3+e^{3 c_1}\right )+3 a b c x^3-2 b^3 x^3\right ){}^2}-a^2 d x^3+a^2 e^{3 c_1}+3 a b c x^3-2 b^3 x^3}+\frac {18 \sqrt [3]{2} \left (1+i \sqrt {3}\right ) x^2 \left (a c-b^2\right )}{\sqrt [3]{\sqrt {-4 x^6 \left (b^2-a c\right )^3+\left (a^2 \left (-d x^3+e^{3 c_1}\right )+3 a b c x^3-2 b^3 x^3\right ){}^2}-a^2 d x^3+a^2 e^{3 c_1}+3 a b c x^3-2 b^3 x^3}}-36 b x}{36 a} \\ y(x)\to \frac {-9\ 2^{2/3} \left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {-4 x^6 \left (b^2-a c\right )^3+\left (a^2 \left (-d x^3+e^{3 c_1}\right )+3 a b c x^3-2 b^3 x^3\right ){}^2}-a^2 d x^3+a^2 e^{3 c_1}+3 a b c x^3-2 b^3 x^3}+\frac {18 i \sqrt [3]{2} \left (\sqrt {3}+i\right ) x^2 \left (b^2-a c\right )}{\sqrt [3]{\sqrt {-4 x^6 \left (b^2-a c\right )^3+\left (a^2 \left (-d x^3+e^{3 c_1}\right )+3 a b c x^3-2 b^3 x^3\right ){}^2}-a^2 d x^3+a^2 e^{3 c_1}+3 a b c x^3-2 b^3 x^3}}-36 b x}{36 a} \\ \end{align*}

✗ Sympy

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

Timed Out