23.1.480 problem 470

Internal problem ID [5087]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 470
Date solved : Tuesday, September 30, 2025 at 11:34:32 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (1+x +2 y\right ) y^{\prime }+7+x -4 y&=0 \end{align*}

✓ Maple. Time used: 0.048 (sec). Leaf size: 196

ode:=(1+x+2*y(x))*diff(y(x),x)+7+x-4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {4 \left (\left (\frac {i \sqrt {3}}{48}-\frac {1}{48}\right ) \left (12 c_1^{2} \sqrt {3}\, \left (3+x \right ) \sqrt {\frac {27 \left (3+x \right )^{2} c_1 -96-32 x}{c_1}}+512+108 \left (3+x \right )^{2} c_1^{2}+\left (-576 x -1728\right ) c_1 \right )^{{2}/{3}}+\left (\frac {1}{3}+\left (-\frac {x}{4}-1\right ) c_1 \right ) \left (12 c_1^{2} \sqrt {3}\, \left (3+x \right ) \sqrt {\frac {27 \left (3+x \right )^{2} c_1 -96-32 x}{c_1}}+512+108 \left (3+x \right )^{2} c_1^{2}+\left (-576 x -1728\right ) c_1 \right )^{{1}/{3}}+\left (1+i \sqrt {3}\right ) \left (-\frac {4}{3}+\left (3+x \right ) c_1 \right )\right )}{\left (12 c_1^{2} \sqrt {3}\, \left (3+x \right ) \sqrt {\frac {27 \left (3+x \right )^{2} c_1 -96-32 x}{c_1}}+512+108 \left (3+x \right )^{2} c_1^{2}+\left (-576 x -1728\right ) c_1 \right )^{{1}/{3}} c_1} \]

✓ Mathematica. Time used: 60.064 (sec). Leaf size: 2617

ode=(1+x+2*y[x])*D[y[x],x]+7+x-4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (x + 2*y(x) + 1)*Derivative(y(x), x) - 4*y(x) + 7,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out