Internal problem ID [154]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Chapter 1 review problems. Page 78
Problem number: 34 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {x +3 y}{y-3 x}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 51
dsolve(diff(y(x),x) = (x+3*y(x))/(-3*x+y(x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {3 c_{1} x -\sqrt {10 c_{1}^{2} x^{2}+1}}{c_{1}} y \left (x \right ) = \frac {3 c_{1} x +\sqrt {10 c_{1}^{2} x^{2}+1}}{c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.482 (sec). Leaf size: 94
DSolve[y'[x] == (x+3*y[x])/(-3*x+y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 3 x-\sqrt {10 x^2+e^{2 c_1}} y(x)\to 3 x+\sqrt {10 x^2+e^{2 c_1}} y(x)\to 3 x-\sqrt {10} \sqrt {x^2} y(x)\to \sqrt {10} \sqrt {x^2}+3 x \end{align*}