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 : Monday, January 27, 2025 at 07:51:03 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*}

✓ Solution by Maple

Time used: 0.149 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

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

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

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