76.4.5 problem 5

Internal problem ID [17399]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.6 (Exact equations and integrating factors). Problems at page 100
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 10:04:39 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=-\frac {4 x +2 y}{2 x +3 y} \end{align*}

✓ Solution by Maple

Time used: 0.174 (sec). Leaf size: 53

dsolve(diff(y(x),x)=-(4*x+2*y(x))/(2*x+3*y(x)),y(x), singsol=all)
 

\begin{align*} y &= \frac {-2 c_{1} x -\sqrt {-8 c_{1}^{2} x^{2}+3}}{3 c_{1}} \\ y &= \frac {-2 c_{1} x +\sqrt {-8 c_{1}^{2} x^{2}+3}}{3 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.510 (sec). Leaf size: 115

DSolve[D[y[x],x]==-(4*x+2*y[x])/(2*x+3*y[x]),y[x],x,IncludeSingularSolutions -> True]
 

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