Internal problem ID [7590]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\left (\sin \left (\ln \relax (x )\right )+\cos \left (\ln \relax (x )\right )+a \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve(diff(y(x),x) - (sin(ln(x)) + cos(ln(x)) +a)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x \left (\sin \left (\ln \relax (x )\right )+a \right )} \]
✓ Solution by Mathematica
Time used: 0.085 (sec). Leaf size: 22
DSolve[y'[x] - (Sin[Log[x]] + Cos[Log[x]] +a)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{x (a+\sin (\log (x)))} \\ y(x)\to 0 \\ \end{align*}