Internal problem ID [2791]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 36.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-6 \,{\mathrm e}^{2 x}+y \tanh \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 27
dsolve(diff(y(x),x) = 6*exp(2*x)-y(x)*tanh(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {3 \sinh \relax (x )+\sinh \left (3 x \right )+3 \cosh \relax (x )+\cosh \left (3 x \right )+c_{1}}{\cosh \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.143 (sec). Leaf size: 33
DSolve[y'[x]==6 Exp[2 x]- y[x] Tanh[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^x \left (6 e^x+2 e^{3 x}+c_1\right )}{e^{2 x}+1} \\ \end{align*}