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Popular Calculus >

y^{''}+4y=x

Solution

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

Solution

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

Solution steps

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

Solve linear ODE:

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

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

Graph

Popular Examples

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\int \frac{4 x ^{3} + 2}{x ^{2}} d x

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\frac{d ^{2}}{d x ^{2}} (sin (5 x))

derivative of y=cot(1-2x^2)

d er i v a t i v e y = cot (1 - 2 x^{2})

xy^'+3y=(2e^{2x})/(x^2)

x y^{^{'}} + 3 y = \frac{2 e ^{2 x}}{x ^{2}}

derivative of cos(x+x^{5/4})

\frac{d}{d x} (cos (x) + x^{\frac{5}{4}})

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+4y=x ?
The solution for y^{''}+4y=x is y=c_{1}cos(2x)+c_{2}sin(2x)+x/4