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 : Tuesday, March 04, 2025 at 07:51:31 PM
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: 1.794 (sec). Leaf size: 226
ode:=(x-3*y(x))*diff(y(x),x)+4+3*x-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 
\[ y \left (x \right ) = \frac {i \left (-36864 \left (x +\frac {3}{2}\right )^{6} c_{1}^{2}+\left (864 c_{1} x^{3}+3888 c_{1} x^{2}+5832 c_{1} x +12 \sqrt {3}\, \sqrt {-16384 \left (-\frac {27}{256}+\left (x +\frac {3}{2}\right )^{3} c_{1} \right ) \left (x +\frac {3}{2}\right )^{6} c_{1}^{2}}+2916 c_{1} \right )^{{4}/{3}}\right ) \sqrt {3}+36864 \left (x +\frac {3}{2}\right )^{6} c_{1}^{2}-48 {\left (12 \sqrt {3}\, \sqrt {-16384 \left (-\frac {27}{256}+\left (x +\frac {3}{2}\right )^{3} c_{1} \right ) \left (x +\frac {3}{2}\right )^{6} c_{1}^{2}}+864 \left (x +\frac {3}{2}\right )^{3} c_{1} \right )}^{{2}/{3}} \left (x +3\right ) \left (3+2 x \right )^{2} c_{1} +\left (864 c_{1} x^{3}+3888 c_{1} x^{2}+5832 c_{1} x +12 \sqrt {3}\, \sqrt {-16384 \left (-\frac {27}{256}+\left (x +\frac {3}{2}\right )^{3} c_{1} \right ) \left (x +\frac {3}{2}\right )^{6} c_{1}^{2}}+2916 c_{1} \right )^{{4}/{3}}}{144 {\left (12 \sqrt {3}\, \sqrt {-16384 \left (-\frac {27}{256}+\left (x +\frac {3}{2}\right )^{3} c_{1} \right ) \left (x +\frac {3}{2}\right )^{6} c_{1}^{2}}+864 \left (x +\frac {3}{2}\right )^{3} c_{1} \right )}^{{2}/{3}} c_{1} \left (3+2 x \right )^{2}} \]
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