12.6.26 problem 26

Internal problem ID [1705]
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 : 26
Date solved : Monday, January 27, 2025 at 05:31:08 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 45

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

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

✓ Solution by Mathematica

Time used: 0.124 (sec). Leaf size: 49

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

\begin{align*} y(x)\to -x-\sqrt {-x^3+x^2+c_1} \\ y(x)\to -x+\sqrt {-x^3+x^2+c_1} \\ \end{align*}