12.7.18 problem 19

Internal problem ID [1728]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page 91
Problem number : 19
Date solved : Tuesday, January 28, 2025 at 02:35:49 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class C`]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 59

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

\begin{align*} y &= \frac {4}{\sqrt {x}\, \sqrt {\frac {c_1 x +48 x^{2}+4}{x}}+2} \\ y &= -\frac {4}{\sqrt {x}\, \sqrt {\frac {c_1 x +48 x^{2}+4}{x}}-2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.772 (sec). Leaf size: 80

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

\begin{align*} y(x)\to \frac {2}{1+\sqrt {-\frac {1}{x^2}} x \sqrt {-12 x^2-4 c_1 x-1}} \\ y(x)\to \frac {2 x}{x+\frac {\sqrt {-12 x^2-4 c_1 x-1}}{\sqrt {-\frac {1}{x^2}}}} \\ y(x)\to 0 \\ \end{align*}