Internal problem ID [11679]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, Miscellaneous Review. Exercises page 60
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-5 y+\left (y+x \right ) y^{\prime }=-3 x} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 47
dsolve((3*x-5*y(x))+(x+y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {6 c_{1} x -\sqrt {8 c_{1} x +1}+1}{2 c_{1}} \\ y \left (x \right ) &= \frac {6 c_{1} x +1+\sqrt {8 c_{1} x +1}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.033 (sec). Leaf size: 80
DSolve[(3*x-5*y[x])+(x+y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (6 x-e^{\frac {c_1}{2}} \sqrt {-8 x+e^{c_1}}-e^{c_1}\right ) \\ y(x)\to \frac {1}{2} \left (6 x+e^{\frac {c_1}{2}} \sqrt {-8 x+e^{c_1}}-e^{c_1}\right ) \\ \end{align*}