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Beliebt Rechnen >

4x^{''}+2x^'+4x=100,x(0)=5,x^'(0)=0

Lösung

4 x^{^{''}} + 2 x^{^{'}} + 4 x = 100, x (0) = 5, x^{^{'}} (0) = 0

Lösung

x = e^{- \frac{t}{4}} (- 20 cos (\frac{15 t}{4}) - \frac{4 5}{3} sin (\frac{15 t}{4})) + 25

Schritte zur Lösung

4 x^{''} (t) + 2 x^{'} (t) + 4 x = 100

Solve linear ODE:

x = e^{- \frac{t}{4}} (- 20 cos (\frac{15 t}{4}) - \frac{4 5}{3} sin (\frac{15 t}{4})) + 25

x = e^{- \frac{t}{4}} (- 20 cos (\frac{15 t}{4}) - \frac{4 5}{3} sin (\frac{15 t}{4})) + 25

Graph

Beliebte Beispiele

limit as x approaches 3 of sqrt(5x^2+2x)

x \to 3 lim (5 x^{2} + 2 x)

x*(dy)/(dx)+y=e^{-x}

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derivative f(x)=(-8x)/(x^2+1)

d er i v a t i v e f (x) = \frac{- 8 x}{x ^{2} + 1}

derivative of (4+3x/(x^2-2x))

\frac{d}{d x} (\frac{4 + 3 x}{x ^{2} - 2 x})

(x+xy^2)dx+e^{x^2}ydy=0

(x + x y^{2}) d x + e^{x^{2}} y d y = 0