Internal problem ID [10617]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number: 22(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {3 x -y-\left (x +y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 51
dsolve((3*x-y(x))-(x+y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {-x c_{1} -\sqrt {4 c_{1}^{2} x^{2}+1}}{c_{1}} \\ y \left (x \right ) = \frac {-x c_{1} +\sqrt {4 c_{1}^{2} x^{2}+1}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.445 (sec). Leaf size: 85
DSolve[(3*x-y[x])-(x+y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x-\sqrt {4 x^2+e^{2 c_1}} \\ y(x)\to -x+\sqrt {4 x^2+e^{2 c_1}} \\ y(x)\to -2 \sqrt {x^2}-x \\ y(x)\to 2 \sqrt {x^2}-x \\ \end{align*}