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Popular >

y^{''}-y=x

Solution

y^{^{''}} - y = x

Solution

y = c_{1} e^{x} + c_{2} e^{- x} - x

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} - x

y = c_{1} e^{x} + c_{2} e^{- x} - x

Graph

Popular Examples

tangent of (2x^{3/2}-x^2+4)/x ,\at x=4 tangent of

\frac{2 x ^{\frac{3}{2}} - x ^{2} + 4}{x}, at x = 4

derivative of 7/(3x^4)

\frac{d}{d x} (\frac{7}{3 x ^{4}})

limit as x approaches 8 of (x-8)/x

x \to 8 lim (\frac{x - 8}{x})

limit as x approaches infinity of (6x^2)/(e^{5x)}

x \to \infty lim (\frac{6 x ^{2}}{e ^{5 x}})

(\partial)/(\partial x)(ln|xy|)

\frac{\partial}{\partial x} (ln ∣ x y ∣)

Frequently Asked Questions (FAQ)

What is the solution for y^{''}-y=x ?
The solution for y^{''}-y=x is y=c_{1}e^x+c_{2}e^{-x}-x