15.4.2 problem 2

Internal problem ID [2915]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 8, page 34
Problem number : 2
Date solved : Monday, January 27, 2025 at 06:55:34 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 53

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

\begin{align*} y &= \frac {-c_1 x -\sqrt {-8 c_1^{2} x^{2}+3}}{3 c_1} \\ y &= \frac {-c_1 x +\sqrt {-8 c_1^{2} x^{2}+3}}{3 c_1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.495 (sec). Leaf size: 119

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

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