4.27.45 \(b y(x)+y''(x)+2 \tanh (x) y'(x)=0\)

ODE
\[ b y(x)+y''(x)+2 \tanh (x) y'(x)=0 \] ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0721108 (sec), leaf count = 54

\[\left \{\left \{y(x)\to \text {sech}(x) \left (c_1 e^{-\sqrt {1-b} x}+\frac {c_2 e^{\sqrt {1-b} x}}{2 \sqrt {1-b}}\right )\right \}\right \}\]

Maple ✓
cpu = 0.087 (sec), leaf count = 34

\[ \left \{ y \left ( x \right ) ={\frac {1}{\cosh \left ( x \right ) } \left ( {\it \_C1}\,\sinh \left ( \sqrt {1-b}x \right ) +{\it \_C2}\,\cosh \left ( \sqrt {1-b}x \right ) \right ) } \right \} \] Mathematica raw input

DSolve[b*y[x] + 2*Tanh[x]*y'[x] + y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (C[1]/E^(Sqrt[1 - b]*x) + (E^(Sqrt[1 - b]*x)*C[2])/(2*Sqrt[1 - b]))*Se
ch[x]}}

Maple raw input

dsolve(diff(diff(y(x),x),x)+2*diff(y(x),x)*tanh(x)+b*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (_C1*sinh((1-b)^(1/2)*x)+_C2*cosh((1-b)^(1/2)*x))/cosh(x)