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Beliebt Rechnen >

y^{''}+y=e^{3t}-4tcos(5t)

Lösung

y^{^{''}} + y = e^{3 t} - 4 t cos (5 t)

Lösung

y = c_{1} cos (t) + c_{2} sin (t) + \frac{1}{10} e^{3 t} + \frac{t cos ( 5 t )}{6} - \frac{5}{72} sin (5 t)

Schritte zur Lösung

y^{''} (t) + y = e^{3 t} - 4 t cos (5 t)

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t) + \frac{1}{10} e^{3 t} + \frac{t cos ( 5 t )}{6} - \frac{5}{72} sin (5 t)

y = c_{1} cos (t) + c_{2} sin (t) + \frac{1}{10} e^{3 t} + \frac{t cos ( 5 t )}{6} - \frac{5}{72} sin (5 t)

Graph

Beliebte Beispiele

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

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

y^{''}-2y^'+y=4x^2-6+x^{-1}e^x

y^{^{''}} - 2 y^{^{'}} + y = 4 x^{2} - 6 + x^{- 1} e^{x}

2y^{''}-4y^'-6y=3e^{2x}

2 y^{^{''}} - 4 y^{^{'}} - 6 y = 3 e^{2 x}

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

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

y^{''}+16y=7sec(4x)

y^{^{''}} + 16 y = 7 sec (4 x)