40.2.12 problem 37

Internal problem ID [6590]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 37
Date solved : Monday, January 27, 2025 at 02:14:32 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 51

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

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

✓ Solution by Mathematica

Time used: 0.456 (sec). Leaf size: 99

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

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