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Beliebt Rechnen >

x^{''}+5x^'+4x=t^2+3t+5

Lösung

x^{^{''}} + 5 x^{^{'}} + 4 x = t^{2} + 3 t + 5

Lösung

x = c_{1} e^{- t} + c_{2} e^{- 4 t} + \frac{t ^{2}}{4} + \frac{t}{8} + \frac{31}{32}

Schritte zur Lösung

x^{''} (t) + 5 x^{'} (t) + 4 x = t^{2} + 3 t + 5

Solve linear ODE:

x = c_{1} e^{- t} + c_{2} e^{- 4 t} + \frac{t ^{2}}{4} + \frac{t}{8} + \frac{31}{32}

x = c_{1} e^{- t} + c_{2} e^{- 4 t} + \frac{t ^{2}}{4} + \frac{t}{8} + \frac{31}{32}

Graph

Beliebte Beispiele

y^{''}-2y^'+y=2sin(3x)

y^{^{''}} - 2 y^{^{'}} + y = 2 sin (3 x)

y^{''}+16y=e^{3t}

y^{^{''}} + 16 y = e^{3 t}

y^{''}+16y=2cos(4x)

y^{^{''}} + 16 y = 2 cos (4 x)

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

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

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

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