What is the general solution for 9sinh(x)-5cosh(x)=15 ?

The general solution for 9sinh(x)-5cosh(x)=15 is x=ln((15+sqrt(281))/4)

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9sinh(x)-5cosh(x)=15

9 sinh (x) - 5 cosh (x) = 15

x = ln (\frac{15 + 281}{4})

Solution steps

9 sinh (x) - 5 cosh (x) = 15

Rewrite using trig identities

9 \cdot \frac{e ^{x} - e ^{- x}}{2} - 5 \cdot \frac{e ^{x} + e ^{- x}}{2} = 15

9 \cdot \frac{e ^{x} - e ^{- x}}{2} - 5 \cdot \frac{e ^{x} + e ^{- x}}{2} = 15 : x = ln (\frac{15 + 281}{4})

x = ln (\frac{15 + 281}{4})

sin (x) - 3 - 3 sin^{2} (x) = 0

cos (2 x) - cos (x) + 1 = 0

4 tan^{2} (x) + 21 tan (x) - 49 = 0

cot (x) = csc (x) + 1

\frac{sin ( 8 )}{30} = \frac{sin ( x )}{120}

What is the general solution for 9sinh(x)-5cosh(x)=15 ?
The general solution for 9sinh(x)-5cosh(x)=15 is x=ln((15+sqrt(281))/4)