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Beliebt Rechnen >

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

Lösung

y^{^{''}} - 4 y^{^{'}} = x \cdot e^{4 x}

Lösung

y = c_{1} e^{4 x} + c_{2} + \frac{e ^{4 x} x ^{2}}{8} - \frac{1}{64} (4 e^{4 x} x - e^{4 x})

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} + \frac{e ^{4 x} x ^{2}}{8} - \frac{1}{64} (4 e^{4 x} x - e^{4 x})

y = c_{1} e^{4 x} + c_{2} + \frac{e ^{4 x} x ^{2}}{8} - \frac{1}{64} (4 e^{4 x} x - e^{4 x})

Graph

Beliebte Beispiele

y^{''}+2y^'+y=e^{-t}(t^3-2t)

y^{^{''}} + 2 y^{^{'}} + y = e^{- t} (t^{3} - 2 t)

(d^2-6d+3)y=e^3x

(d^{2} - 6 d + 3) y = e^{3} x

y^{''}+4y^'+3y=6

y^{^{''}} + 4 y^{^{'}} + 3 y = 6

y^{''}+4y=1,6ty(0)=3,y^'(0)=-6

y^{^{''}} + 4 y = 1, 6 t y (0) = 3, y^{^{'}} (0) = - 6

y^{''}+2y^'+2y=acos(bt)

y^{^{''}} + 2 y^{^{'}} + 2 y = a cos (b t)