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Popular Calculus >

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

Solution

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

Solution

y = e^{\frac{x}{2}} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + e^{- \frac{x}{2}} (c_{3} cos (\frac{x}{2}) + c_{4} sin (\frac{x}{2})) + \frac{1}{2} cos (x)

Solution steps

y^{(4)} (x) + y = cos (x)

Solve linear ODE:

y = e^{\frac{x}{2}} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + e^{- \frac{x}{2}} (c_{3} cos (\frac{x}{2}) + c_{4} sin (\frac{x}{2})) + \frac{1}{2} cos (x)

y = e^{\frac{x}{2}} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + e^{- \frac{x}{2}} (c_{3} cos (\frac{x}{2}) + c_{4} sin (\frac{x}{2})) + \frac{1}{2} cos (x)

Graph

Popular Examples

y^{''}-4y^'+5y=4e^{3t},y(0)=2,y^'(0)=7

y^{'''}-2y^{''}-5y^'+6y=e^x+x^2

x^{''}+3x^'+2x=sin(3t)

x^{''}+8x^'+16=0

x^{''''}-x^{''}=1

Frequently Asked Questions (FAQ)

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