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Beliebt Rechnen >

y^{''}+4y^'=t^2+6e^t,y(0)=0,y^'(0)=9

Lösung

y^{^{''}} + 4 y^{^{'}} = t^{2} + 6 e^{t}, y (0) = 0, y^{^{'}} (0) = 9

Lösung

y = \frac{1243}{640} - \frac{6}{5} - \frac{1243}{640} e^{- 4 t} + \frac{t ^{3}}{12} - \frac{t ^{2}}{16} + \frac{t}{32} + \frac{6}{5} e^{t}

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) = t^{2} + 6 e^{t}

Solve linear ODE:

y = \frac{1243}{640} - \frac{6}{5} - \frac{1243}{640} e^{- 4 t} + \frac{t ^{3}}{12} - \frac{t ^{2}}{16} + \frac{t}{32} + \frac{6}{5} e^{t}

y = \frac{1243}{640} - \frac{6}{5} - \frac{1243}{640} e^{- 4 t} + \frac{t ^{3}}{12} - \frac{t ^{2}}{16} + \frac{t}{32} + \frac{6}{5} e^{t}

Graph

Beliebte Beispiele

y^{''}+4y^'=t^2+6e^t,y(0)=0,y^'(0)=5

y^{^{''}} + 4 y^{^{'}} = t^{2} + 6 e^{t}, y (0) = 0, y^{^{'}} (0) = 5

y^{''}+y=t^2sin(t)

y^{^{''}} + y = t^{2} sin (t)

y^{'''}-8y^{''}+5y^'+y=5t

y^{^{'''}} - 8 y^{^{''}} + 5 y^{^{'}} + y = 5 t

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

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

D (x) = 120 x - 3580