ODE
\[ y'(x)=6 e^{2 x}-y(x) \tanh (x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.193033 (sec), leaf count = 33
\[\left \{\left \{y(x)\to \frac {e^x \left (6 e^x+2 e^{3 x}+c_1\right )}{e^{2 x}+1}\right \}\right \}\]
Maple ✓
cpu = 0.033 (sec), leaf count = 27
\[\left [y \left (x \right ) = \frac {3 \sinh \left (x \right )+\sinh \left (3 x \right )+3 \cosh \left (x \right )+\cosh \left (3 x \right )+\textit {\_C1}}{\cosh \left (x \right )}\right ]\] 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))
Maple raw output
[y(x) = (3*sinh(x)+sinh(3*x)+3*cosh(x)+cosh(3*x)+_C1)/cosh(x)]