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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{1}{7} e^{2 t} + \frac{t cos ( 3 t )}{3} - \frac{1}{3} sin (3 t)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{1}{7} e^{2 t} + \frac{t cos ( 3 t )}{3} - \frac{1}{3} sin (3 t)

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{1}{7} e^{2 t} + \frac{t cos ( 3 t )}{3} - \frac{1}{3} sin (3 t)

Graph

Beliebte Beispiele

y^{''}-4y^'+3y=x^2e^x

y^{^{''}} - 4 y^{^{'}} + 3 y = x^{2} e^{x}

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

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

y^{''}+9y=2csc^2(3x)

y^{^{''}} + 9 y = 2 csc^{2} (3 x)

y^{''}+4y^'+3y=1,y^'(0)=1

y^{^{''}} + 4 y^{^{'}} + 3 y = 1, y^{^{'}} (0) = 1

(D^2-3D+2)y=e^x

(D^{2} - 3 D + 2) y = e^{x}