Solve (d^2u/dx^2) = -k^2x

Evaluate

d^{2} \times \frac{u}{d x ^{2}} = - k^{2} x

Multiply the terms

More Steps

\frac{d u}{x ^{2}} = - k^{2} x

Cross multiply

d u = x^{2} (- k^{2} x)

Simplify the equation

d u = - k^{2} x^{3}

Swap the sides of the equation

- k^{2} x^{3} = d u

Divide both sides

\frac{- k ^{2} x ^{3}}{- k ^{2}} = \frac{d u}{- k ^{2}}

Divide the numbers

x^{3} = \frac{d u}{- k ^{2}}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x^{3} = - \frac{d u}{k ^{2}}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 - \frac{d u}{k ^{2}}

Calculate

x = 3 - \frac{d u}{k ^{2}}

Simplify the root

More Steps

x = \frac{3 - d u k}{k}

Solution

More Steps

x = - \frac{3 d u k}{k}

(d^2u/dx^2) = K^2x