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]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x +3 y}{-3 x +y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 51
dsolve(diff(y(x),x) = (x+3*y(x))/(-3*x+y(x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {3 x c_{1}-\sqrt {10 c_{1}^{2} x^{2}+1}}{c_{1}} \\ y \relax (x ) = \frac {3 x c_{1}+\sqrt {10 c_{1}^{2} x^{2}+1}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.197 (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*}