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Beliebt Rechnen >

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

Lösung

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

Lösung

y = - \frac{43}{40} cos (2 t) - \frac{3}{5} sin (2 t) + \frac{t ^{2}}{4} - \frac{1}{8} + \frac{6}{5} e^{t}

Schritte zur Lösung

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

Solve linear ODE:

y = - \frac{43}{40} cos (2 t) - \frac{3}{5} sin (2 t) + \frac{t ^{2}}{4} - \frac{1}{8} + \frac{6}{5} e^{t}

y = - \frac{43}{40} cos (2 t) - \frac{3}{5} sin (2 t) + \frac{t ^{2}}{4} - \frac{1}{8} + \frac{6}{5} e^{t}

Graph

Beliebte Beispiele

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

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

x^{''}+x=9cos(4t)

x^{^{''}} + x = 9 cos (4 t)

y^{''}-4y=3e^{2t}

y^{^{''}} - 4 y = 3 e^{2 t}

9y^{''}+7y^'-y=24

9 y^{^{''}} + 7 y^{^{'}} - y = 24

y^{''}+16y=8x+8sin(x)

y^{^{''}} + 16 y = 8 x + 8 sin (x)