4.1.37 \(y'(x)=6 e^{2 x}-y(x) \tanh (x)\)

ODE
\[ y'(x)=6 e^{2 x}-y(x) \tanh (x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0194598 (sec), leaf count = 33

\[\left \{\left \{y(x)\to \frac {e^x \left (c_1+6 e^x+2 e^{3 x}\right )}{e^{2 x}+1}\right \}\right \}\]

Maple
cpu = 0.026 (sec), leaf count = 27

\[ \left \{ y \relax (x ) ={\frac {\cosh \left (3\,x \right ) +3\,\cosh \relax (x ) +\sinh \left (3\,x \right ) +3\,\sinh \relax (x ) +{\it \_C1}}{\cosh \relax (x ) }} \right \} \] Mathematica raw input

DSolve[y'[x] == 6*E^(2*x) - Tanh[x]*y[x],y[x],x]

Mathematica raw output

{{y[x] -> (E^x*(6*E^x + 2*E^(3*x) + C[1]))/(1 + E^(2*x))}}

Maple raw input

dsolve(diff(y(x),x) = 6*exp(2*x)-y(x)*tanh(x), y(x),'implicit')

Maple raw output

y(x) = (cosh(3*x)+3*cosh(x)+sinh(3*x)+3*sinh(x)+_C1)/cosh(x)