8.5.31 problem 31

Internal problem ID [759]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 31
Date solved : Monday, January 27, 2025 at 03:03:34 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x +3 y+\left (3 x +2 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 53

dsolve(2*x+3*y(x)+(3*x+2*y(x))*diff(y(x),x) = 0,y(x), singsol=all)
 

\begin{align*} y &= \frac {-3 c_1 x -\sqrt {5 c_1^{2} x^{2}+4}}{2 c_1} \\ y &= \frac {-3 c_1 x +\sqrt {5 c_1^{2} x^{2}+4}}{2 c_1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.401 (sec). Leaf size: 110

DSolve[2*x+3*y[x]+(3*x+2*y[x])*D[y[x],x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{2} \left (-3 x-\sqrt {5 x^2+4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (-3 x+\sqrt {5 x^2+4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (-\sqrt {5} \sqrt {x^2}-3 x\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {5} \sqrt {x^2}-3 x\right ) \\ \end{align*}