20.4.16 problem Problem 25

Internal problem ID [3651]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 25
Date solved : Sunday, March 30, 2025 at 01:58:47 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {4 y-2 x}{x +y} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Maple. Time used: 0.312 (sec). Leaf size: 72

ode:=diff(y(x),x) = 2*(2*y(x)-x)/(x+y(x)); 
ic:=y(0) = 2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {\left (3 \sqrt {3}\, x \sqrt {x \left (27 x +8\right )}+27 x^{2}+36 x +8\right )^{{1}/{3}}}{3}+\frac {4 x +\frac {4}{3}}{\left (3 \sqrt {3}\, x \sqrt {x \left (27 x +8\right )}+27 x^{2}+36 x +8\right )^{{1}/{3}}}+2 x +\frac {2}{3} \]

✓ Mathematica. Time used: 60.269 (sec). Leaf size: 121

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

\[ y(x)\to \frac {1}{3} \left (x \left (\frac {12}{\sqrt [3]{3 \sqrt {3} \sqrt {x^3 (27 x+8)}+27 x^2+36 x+8}}+6\right )+\sqrt [3]{3 \sqrt {3} \sqrt {x^3 (27 x+8)}+27 x^2+36 x+8}+\frac {4}{\sqrt [3]{3 \sqrt {3} \sqrt {x^3 (27 x+8)}+27 x^2+36 x+8}}+2\right ) \]

✗ Sympy

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

Timed Out