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Popular Calculus >

y^{''}-y= 1/(cosh(x))

Solution

y^{^{''}} - y = \frac{1}{cosh ( x )}

Solution

y = c_{1} e^{x} + c_{2} e^{- x} + e^{x} \cdot \int \frac{e ^{- x} sech ( x )}{2} d x + e^{- x} (- \frac{1}{2} e^{x} sech (x) + \frac{1}{2} sech (x) arcsech (sech (x)) + arcsin (\frac{2}{2} sech (x) + 1))

Solution steps

y^{''} (x) - y = \frac{1}{cosh ( x )}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + e^{x} \cdot \int \frac{e ^{- x} sech ( x )}{2} d x + e^{- x} (- \frac{1}{2} e^{x} sech (x) + \frac{1}{2} sech (x) arcsech (sech (x)) + arcsin (\frac{2}{2} sech (x) + 1))

y = c_{1} e^{x} + c_{2} e^{- x} + e^{x} \cdot \int \frac{e ^{- x} sech ( x )}{2} d x + e^{- x} (- \frac{1}{2} e^{x} sech (x) + \frac{1}{2} sech (x) arcsech (sech (x)) + arcsin (\frac{2}{2} sech (x) + 1))

Popular Examples

x^{''}+2x^'+x=e^{-2t},x(0)=2

y^{''}+4y^'+13y=cos(3x)

4y^{''}-y=sin(x)

y^{''}+4y^'+4y=6x+7

y^{'''}+y^{''}+y^'+y=sin(3x)

Frequently Asked Questions (FAQ)

What is the solution for y^{''}-y= 1/(cosh(x)) ?
The solution for y^{''}-y= 1/(cosh(x)) is