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Beliebt Rechnen >

y^{''}-4y=te^{4t}

Lösung

y^{^{''}} - 4 y = t e^{4 t}

Lösung

y = c_{1} e^{2 t} + c_{2} e^{- 2 t} + \frac{e ^{4 t} t}{12} - \frac{1}{18} e^{4 t}

Schritte zur Lösung

y^{''} (t) - 4 y = t e^{4 t}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- 2 t} + \frac{e ^{4 t} t}{12} - \frac{1}{18} e^{4 t}

y = c_{1} e^{2 t} + c_{2} e^{- 2 t} + \frac{e ^{4 t} t}{12} - \frac{1}{18} e^{4 t}

Graph

Beliebte Beispiele

y^{''}+y^'+256/3 x=50cos(3x)

y^{^{''}} + y^{^{'}} + \frac{256}{3} x = 50 cos (3 x)

y^{''}-3y^'+y=x^2+x

y^{^{''}} - 3 y^{^{'}} + y = x^{2} + x

y^{''}+2y^'=e^t

y^{^{''}} + 2 y^{^{'}} = e^{t}

y^{''}-6y^'+8y=e^{-3t}

y^{^{''}} - 6 y^{^{'}} + 8 y = e^{- 3 t}

y^{''}-y^'+2y=x+sin(x)

y^{^{''}} - y^{^{'}} + 2 y = x + sin (x)