64.3.5 problem 5

Internal problem ID [13276]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises page 37
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 05:13:59 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 6 y x +2 y^{2}-5+\left (3 x^{2}+4 y x -6\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 69

dsolve((6*x*y(x)+2*y(x)^2-5)+(3*x^2+4*x*y(x)-6)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {-3 x^{2}+6+\sqrt {9 x^{4}-8 c_{1} x +4 x^{2}+36}}{4 x} \\ y &= \frac {-3 x^{2}+6-\sqrt {9 x^{4}-8 c_{1} x +4 x^{2}+36}}{4 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.608 (sec). Leaf size: 79

DSolve[(6*x*y[x]+2*y[x]^2-5)+(3*x^2+4*x*y[x]-6)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {3 x^2+\sqrt {9 x^4+4 x^2+16 c_1 x+36}-6}{4 x} \\ y(x)\to \frac {-3 x^2+\sqrt {9 x^4+4 x^2+16 c_1 x+36}+6}{4 x} \\ \end{align*}