12.6.9 problem 9

Internal problem ID [1688]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number : 9
Date solved : Monday, January 27, 2025 at 05:27:59 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 3 x^{2}+2 y x +4 y^{2}+\left (x^{2}+8 y x +18 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 77

dsolve((3*x^2+2*x*y(x)+4*y(x)^2)+(x^2+8*x*y(x)+18*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {-x^{2}+\sqrt {-15 x^{4}-36 x^{3}-16 c_1 x -36 c_1}}{8 x +18} \\ y &= \frac {-x^{2}-\sqrt {-15 x^{4}-36 x^{3}-16 c_1 x -36 c_1}}{8 x +18} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.575 (sec). Leaf size: 84

DSolve[(3*x^2+2*x*y[x]+4*y[x]^2)+(x^2+8*x*y[x]+18*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x^2+\sqrt {-15 x^4-36 x^3+16 c_1 x+36 c_1}}{8 x+18} \\ y(x)\to \frac {-x^2+\sqrt {-15 x^4-36 x^3+16 c_1 x+36 c_1}}{8 x+18} \\ \end{align*}