Internal problem ID [4262]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page
403
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+y \tanh \relax (x )-2 \,{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 26
dsolve(diff(y(x),x)+y(x)*tanh(x)=2*exp(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\cosh \left (2 x \right )+1+\sinh \left (2 x \right )+2 x +2 c_{1}}{2 \cosh \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.127 (sec). Leaf size: 29
DSolve[y'[x]+y[x]*Tanh[x]==2*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^x \left (2 x+e^{2 x}+c_1\right )}{e^{2 x}+1} \\ \end{align*}