29.18.2 problem 478

Internal problem ID [5076]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 478
Date solved : Sunday, March 30, 2025 at 06:35:33 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x -3 y\right ) y^{\prime }+4+3 x -y&=0 \end{align*}

✓ Maple. Time used: 0.231 (sec). Leaf size: 296

ode:=(x-3*y(x))*diff(y(x),x)+4+3*x-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\frac {3 \left (-3+32 \left (x +\frac {3}{2}\right )^{2} \left (x +1\right ) c_1^{3}\right ) \left (12 \sqrt {81-768 \left (x +\frac {3}{2}\right )^{3} c_1^{3}}+108+\left (-512 x^{3}-2304 x^{2}-3456 x -1728\right ) c_1^{3}\right )^{{2}/{3}}}{512}+6 c_1 \left (x +1\right ) \left (\frac {\left (-\frac {\sqrt {81-768 \left (x +\frac {3}{2}\right )^{3} c_1^{3}}}{128}-\frac {9}{128}+\left (x +\frac {3}{2}\right )^{3} c_1^{3}\right ) \left (1+i \sqrt {3}\right ) \left (12 \sqrt {81-768 \left (x +\frac {3}{2}\right )^{3} c_1^{3}}+108+\left (-512 x^{3}-2304 x^{2}-3456 x -1728\right ) c_1^{3}\right )^{{1}/{3}}}{8}+\left (x +\frac {3}{2}\right ) c_1 \left (-\frac {\sqrt {81-768 \left (x +\frac {3}{2}\right )^{3} c_1^{3}}}{64}-\frac {9}{64}+\left (x +\frac {3}{2}\right )^{3} c_1^{3}\right ) \left (i \sqrt {3}-1\right )\right )}{{\left (\frac {\left (1-i \sqrt {3}\right ) \left (12 \sqrt {81-768 \left (x +\frac {3}{2}\right )^{3} c_1^{3}}+108+\left (-512 x^{3}-2304 x^{2}-3456 x -1728\right ) c_1^{3}\right )^{{2}/{3}}}{64}+\left (x +\frac {3}{2}\right ) c_1 \left (\frac {\left (12 \sqrt {81-768 \left (x +\frac {3}{2}\right )^{3} c_1^{3}}+108+\left (-512 x^{3}-2304 x^{2}-3456 x -1728\right ) c_1^{3}\right )^{{1}/{3}}}{4}+\left (x +\frac {3}{2}\right ) c_1 \left (1+i \sqrt {3}\right )\right )\right )}^{2} c_1} \]

✓ Mathematica. Time used: 60.043 (sec). Leaf size: 793

ode=(x-3 y[x])D[y[x],x]+4+3 x-y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x + (x - 3*y(x))*Derivative(y(x), x) - y(x) + 4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out