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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} + c_{2} e^{- t} + \frac{3 e ^{t} t ^{2}}{2} - \frac{7 e ^{t} t}{2} + \frac{15}{4} e^{t}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- t} + \frac{3 e ^{t} t ^{2}}{2} - \frac{7 e ^{t} t}{2} + \frac{15}{4} e^{t}

y = c_{1} + c_{2} e^{- t} + \frac{3 e ^{t} t ^{2}}{2} - \frac{7 e ^{t} t}{2} + \frac{15}{4} e^{t}

Graph

Beliebte Beispiele

y^{''}+4y=5e^x-4x^2

y^{^{''}} + 4 y = 5 e^{x} - 4 x^{2}

y^{^{''}} + x + y = 0

y^{''}+y=1,y(0)=0,y(1)=0

y^{^{''}} + y = 1, y (0) = 0, y (1) = 0

y^{''}+12y^'+27y=64e^{-1t}

y^{^{''}} + 12 y^{^{'}} + 27 y = 64 e^{- 1 t}

2y^{''}-6y^'=5,y(0)=2,y^'(0)=1

2 y^{^{''}} - 6 y^{^{'}} = 5, y (0) = 2, y^{^{'}} (0) = 1