29.23.6 problem 637
Internal
problem
ID
[5228]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
23
Problem
number
:
637
Date
solved
:
Sunday, March 30, 2025 at 06:56:40 AM
CAS
classification
:
[[_homogeneous, `class A`], _exact, _rational, _dAlembert]
\begin{align*} \left (a \,x^{2}+2 b x y+c y^{2}\right ) y^{\prime }+k \,x^{2}+2 a x y+b y^{2}&=0 \end{align*}
✓ Maple. Time used: 0.020 (sec). Leaf size: 1107
ode:=(x^2*a+2*b*x*y(x)+c*y(x)^2)*diff(y(x),x)+k*x^2+2*a*x*y(x)+b*y(x)^2 = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*} \text {Solution too large to show}\end{align*}
✓ Mathematica. Time used: 60.368 (sec). Leaf size: 744
ode=(a x^2+2 b x y[x]+c y[x]^2)D[y[x],x]+k x^2+2 a x y[x]+b y[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 (3 a b c x^3-2 b^3 x^3+c^2 \left (-k x^3+e^{3 c_1}\right )\right ){}^2}+3 a b c x^3-2 b^3 x^3-c^2 k x^3+c^2 e^{3 c_1}}+\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 (3 a b c x^3-2 b^3 x^3+c^2 \left (-k x^3+e^{3 c_1}\right )\right ){}^2}+3 a b c x^3-2 b^3 x^3-c^2 k x^3+c^2 e^{3 c_1}}}-2 b x}{2 c} \\
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 (3 a b c x^3-2 b^3 x^3+c^2 \left (-k x^3+e^{3 c_1}\right )\right ){}^2}+3 a b c x^3-2 b^3 x^3-c^2 k x^3+c^2 e^{3 c_1}}+\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 (3 a b c x^3-2 b^3 x^3+c^2 \left (-k x^3+e^{3 c_1}\right )\right ){}^2}+3 a b c x^3-2 b^3 x^3-c^2 k x^3+c^2 e^{3 c_1}}}-36 b x}{36 c} \\
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 (3 a b c x^3-2 b^3 x^3+c^2 \left (-k x^3+e^{3 c_1}\right )\right ){}^2}+3 a b c x^3-2 b^3 x^3-c^2 k x^3+c^2 e^{3 c_1}}+\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 (3 a b c x^3-2 b^3 x^3+c^2 \left (-k x^3+e^{3 c_1}\right )\right ){}^2}+3 a b c x^3-2 b^3 x^3-c^2 k x^3+c^2 e^{3 c_1}}}-36 b x}{36 c} \\
\end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
a = symbols("a")
b = symbols("b")
c = symbols("c")
k = symbols("k")
y = Function("y")
ode = Eq(2*a*x*y(x) + b*y(x)**2 + k*x**2 + (a*x**2 + 2*b*x*y(x) + c*y(x)**2)*Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out