20.4.17 problem Problem 26

Internal problem ID [3652]
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 26
Date solved : Sunday, March 30, 2025 at 01:59:02 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Maple. Time used: 0.117 (sec). Leaf size: 19

ode:=diff(y(x),x) = (2*x-y(x))/(x+4*y(x)); 
ic:=y(1) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {x}{4}+\frac {\sqrt {9 x^{2}+16}}{4} \]

✓ Mathematica. Time used: 0.418 (sec). Leaf size: 24

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

\[ y(x)\to \frac {1}{4} \left (\sqrt {9 x^2+16}-x\right ) \]

✓ Sympy. Time used: 1.132 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = - \frac {x}{4} + \frac {\sqrt {9 x^{2} + 16}}{4} \]