Internal problem ID [7586]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+y \cos \relax (x )-{\mathrm e}^{2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 21
dsolve(diff(y(x),x) + y(x)*cos(x) - exp(2*x)=0,y(x), singsol=all)
\[ y \relax (x ) = \left (\int {\mathrm e}^{2 x +\sin \relax (x )}d x +c_{1}\right ) {\mathrm e}^{-\sin \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.074 (sec). Leaf size: 32
DSolve[y'[x] + y[x]*Cos[x] - Exp[2*x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-\sin (x)} \left (\int _1^xe^{2 K[1]+\sin (K[1])}dK[1]+c_1\right ) \\ \end{align*}