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Popular >

y^{''}+y=cosh(x)

Solution

y^{^{''}} + y = cosh (x)

Solution

y = c_{1} cos (x) + c_{2} sin (x) + \frac{1}{4} e^{- x} cos^{2} (x) + \frac{1}{4} e^{- x} cos (x) sin (x) + \frac{1}{4} e^{x} cos^{2} (x) - \frac{1}{4} e^{x} cos (x) sin (x) + \frac{sin ( x ) ( sin ( x ) cosh ( x ) + cos ( x ) sinh ( x ) )}{2}

Solution steps

y^{''} (x) + y = cosh (x)

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + \frac{1}{4} e^{- x} cos^{2} (x) + \frac{1}{4} e^{- x} cos (x) sin (x) + \frac{1}{4} e^{x} cos^{2} (x) - \frac{1}{4} e^{x} cos (x) sin (x) + \frac{sin ( x ) ( sin ( x ) cosh ( x ) + cos ( x ) sinh ( x ) )}{2}

y = c_{1} cos (x) + c_{2} sin (x) + \frac{1}{4} e^{- x} cos^{2} (x) + \frac{1}{4} e^{- x} cos (x) sin (x) + \frac{1}{4} e^{x} cos^{2} (x) - \frac{1}{4} e^{x} cos (x) sin (x) + \frac{sin ( x ) ( sin ( x ) cosh ( x ) + cos ( x ) sinh ( x ) )}{2}

Graph

Popular Examples

(D^2+D-2)y=2x-40cos(2x)

(D^{2} + D - 2) y = 2 x - 40 cos (2 x)

y^{''''}+16y^{''}=sin(4t)+te^{5t}+4

y^{^{''''}} + 16 y^{^{''}} = sin (4 t) + t e^{5 t} + 4

y^{''}-4y^'+3y=e^{3x}

y^{^{''}} - 4 y^{^{'}} + 3 y = e^{3 x}

y^{''}+9y=t^2e^{3t}+6

y^{^{''}} + 9 y = t^{2} e^{3 t} + 6

y^{'''}+2y^{''}-13y^'+10y=xe^{-x}

y^{^{'''}} + 2 y^{^{''}} - 13 y^{^{'}} + 10 y = x e^{- x}

Frequently Asked Questions (FAQ)

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