15.2.4 problem 4

Internal problem ID [2874]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 6, page 25
Problem number : 4
Date solved : Monday, January 27, 2025 at 06:21:31 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*}

✓ Solution by Maple

Time used: 0.035 (sec). Leaf size: 53

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

\begin{align*} y &= \frac {-c_1 x -\sqrt {9 c_1^{2} x^{2}+8}}{4 c_1} \\ y &= \frac {-c_1 x +\sqrt {9 c_1^{2} x^{2}+8}}{4 c_1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.418 (sec). Leaf size: 101

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

\begin{align*} y(x)\to \frac {1}{4} \left (-x-\sqrt {9 x^2+8 e^{c_1}}\right ) \\ y(x)\to \frac {1}{4} \left (-x+\sqrt {9 x^2+8 e^{c_1}}\right ) \\ y(x)\to \frac {1}{4} \left (-3 \sqrt {x^2}-x\right ) \\ y(x)\to \frac {1}{4} \left (3 \sqrt {x^2}-x\right ) \\ \end{align*}