10.5.25 problem 32

Internal problem ID [1217]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 32
Date solved : Monday, January 27, 2025 at 04:45:35 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 59

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

\begin{align*} y &= \frac {-c_1 \,x^{2}-\sqrt {x^{4} c_1^{2}+1}}{c_1 x} \\ y &= \frac {-c_1 \,x^{2}+\sqrt {x^{4} c_1^{2}+1}}{c_1 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.643 (sec). Leaf size: 93

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

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