64.7.1 problem 1

Internal problem ID [13375]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Section 2.4. Special integrating factors and transformations. Exercises page 67
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 05:36:02 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 5 y x +4 y^{2}+1+\left (2 y x +x^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 59

dsolve((5*x*y(x)+4*y(x)^2+1)+(x^2+2*x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.706 (sec). Leaf size: 84

DSolve[(5*x*y[x]+4*y[x]^2+1)+(x^2+2*x*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x^5+\sqrt {x^3} \sqrt {x^7-x^5+4 c_1 x}}{2 x^4} \\ y(x)\to -\frac {x}{2}+\frac {\sqrt {x^3} \sqrt {x^7-x^5+4 c_1 x}}{2 x^4} \\ \end{align*}