Internal problem ID [2068]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.8, page 68
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y^{\prime } x -y-\sqrt {9 x^{2}+y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(x*diff(y(x),x)-y(x)=sqrt(9*x^2+y(x)^2),y(x), singsol=all)
\[ \frac {y \left (x \right )}{x^{2}}+\frac {\sqrt {9 x^{2}+y \left (x \right )^{2}}}{x^{2}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.351 (sec). Leaf size: 27
DSolve[x*y'[x]-y[x]==Sqrt[9*x^2+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {9 e^{c_1} x^2}{2}-\frac {e^{-c_1}}{2} \\ \end{align*}