Internal problem ID [2067]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.8, page 68
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y^{\prime } x -\sqrt {16 x^{2}-y^{2}}-y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(x*diff(y(x),x)=sqrt(16*x^2-y(x)^2)+y(x),y(x), singsol=all)
\[ -\arctan \left (\frac {y \left (x \right )}{\sqrt {16 x^{2}-y \left (x \right )^{2}}}\right )+\ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.384 (sec). Leaf size: 18
DSolve[x*y'[x]==Sqrt[16*x^2-y[x]^2]+y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -4 x \cosh (i \log (x)+c_1) \\ \end{align*}