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Beliebt Rechnen >

y^{''}-y=9e^{5t}+6te^{5t}+3t^2e^{5t}

Lösung

y^{^{''}} - y = 9 e^{5 t} + 6 t e^{5 t} + 3 t^{2} e^{5 t}

Lösung

y = c_{1} e^{t} + c_{2} e^{- t} + \frac{72 e ^{5 t} t ^{2} + 84 e ^{5 t} t + 175 e ^{5 t}}{576}

Schritte zur Lösung

y^{''} (t) - y = 9 e^{5 t} + 6 t e^{5 t} + 3 t^{2} e^{5 t}

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{- t} + \frac{72 e ^{5 t} t ^{2} + 84 e ^{5 t} t + 175 e ^{5 t}}{576}

y = c_{1} e^{t} + c_{2} e^{- t} + \frac{72 e ^{5 t} t ^{2} + 84 e ^{5 t} t + 175 e ^{5 t}}{576}

Graph

Beliebte Beispiele

limit as x approaches 0 of \sqrt[3]{3x}

x \to 0 lim (3 3 x)

derivative of x^2+2/x

\frac{d}{d x} (x^{2} + \frac{2}{x})

integral of (3-e^x)/(e^{5x)}

\int \frac{3 - e ^{x}}{e ^{5 x}} d x

integral of 3-4/(2x+1)

\int 3 - \frac{4}{2 x + 1} d x

f(x)=3x^5-4x^4+9x-6

f (x) = 3 x^{5} - 4 x^{4} + 9 x - 6