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Beliebt Rechnen >

y^{''}+4y^'+5y=-15x+3e^{-x}

Lösung

y^{^{''}} + 4 y^{^{'}} + 5 y = - 15 x + 3 e^{- x}

Lösung

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) - 3 x + \frac{12}{5} + \frac{3}{2} e^{- x}

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 5 y = - 15 x + 3 e^{- x}

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) - 3 x + \frac{12}{5} + \frac{3}{2} e^{- x}

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) - 3 x + \frac{12}{5} + \frac{3}{2} e^{- x}

Graph

Beliebte Beispiele

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

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

y^{''}-4y^'-5y=2+e^{-t}

y^{^{''}} - 4 y^{^{'}} - 5 y = 2 + e^{- t}

y^{''}+16y=e^{-4t}+3sin(4t)

y^{^{''}} + 16 y = e^{- 4 t} + 3 sin (4 t)

y^{''}-4y=-6cos(4x)+2sin(4x)

y^{^{''}} - 4 y = - 6 cos (4 x) + 2 sin (4 x)

y^{''}+3y^'+2y= 1/((5+e^x))

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{( 5 + e ^{x} )}