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Beliebt Rechnen >

y^{''}-y=e^xcos(x),y(0)=0,y^'(0)=0

Lösung

y^{^{''}} - y = e^{x} cos (x), y (0) = 0, y^{^{'}} (0) = 0

Lösung

y = \frac{1}{5} e^{- x} + \frac{2}{5} e^{x} sin (x) - \frac{1}{5} e^{x} cos (x)

Schritte zur Lösung

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

Solve linear ODE:

y = \frac{1}{5} e^{- x} + \frac{2}{5} e^{x} sin (x) - \frac{1}{5} e^{x} cos (x)

y = \frac{1}{5} e^{- x} + \frac{2}{5} e^{x} sin (x) - \frac{1}{5} e^{x} cos (x)

Graph

Beliebte Beispiele

y^{''}-10y^'+25y=t^{-6}e^{5t}

y^{^{''}} - 10 y^{^{'}} + 25 y = t^{- 6} e^{5 t}

y^{''}-y^'-2y=xe^{4x}

y^{^{''}} - y^{^{'}} - 2 y = x e^{4 x}

q^{''}+100q^'+2500q=40,q(0)=0

q^{^{''}} + 100 q^{^{'}} + 2500 q = 40, q (0) = 0

(D^2+5)y=cos(sqrt(5))x

(D^{2} + 5) y = cos (5) x

3y^'+2y^{''}=-1000cos(3.14*t/(0.2))

3 y^{^{'}} + 2 y^{^{''}} = - 1000 cos (3.14 \cdot \frac{t}{0.2})