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Beliebt Rechnen >

y^{''}-4y=e^{2x},y(0)=0,y^'(0)=0

Lösung

y^{^{''}} - 4 y = e^{2 x}, y (0) = 0, y^{^{'}} (0) = 0

Lösung

y = - \frac{1}{16} e^{2 x} + \frac{1}{16} e^{- 2 x} + \frac{e ^{2 x} x}{4}

Schritte zur Lösung

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

Solve linear ODE:

y = - \frac{1}{16} e^{2 x} + \frac{1}{16} e^{- 2 x} + \frac{e ^{2 x} x}{4}

y = - \frac{1}{16} e^{2 x} + \frac{1}{16} e^{- 2 x} + \frac{e ^{2 x} x}{4}

Graph

Beliebte Beispiele

y^{''}-3y^'-28y=1056e^{-t}

y^{^{''}} - 3 y^{^{'}} - 28 y = 1056 e^{- t}

y^{''}+y=g(t),y(0)=0,y^'(0)=0

y^{^{''}} + y = g (t), y (0) = 0, y^{^{'}} (0) = 0

y^{''}+6y^'+18y=11te^{4t}

y^{^{''}} + 6 y^{^{'}} + 18 y = 11 t e^{4 t}

(d^2y)/(dx^2)-(dy)/(dx)-2y=8

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 2 y = 8

y^{''}-10y^'+25y=6+3x

y^{^{''}} - 10 y^{^{'}} + 25 y = 6 + 3 x