(d^2+3d+2)y=sin(e^x)

Lösung

(d^{2} + 3 d + 2) y = sin (e^{x})

y = c_{1} e^{- x} + c_{2} e^{- 2 x} - e^{- 2 x} sin (e^{x})

Schritte zur Lösung

(d^{2} + 3 d + 2) y = sin (e^{x})

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} - e^{- 2 x} sin (e^{x})

y = c_{1} e^{- x} + c_{2} e^{- 2 x} - e^{- 2 x} sin (e^{x})

(d^{3} + 8) y = x^{4} + x + 1

(d^{2} + d + 1) y = x^{3}

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

(d^{2} + 3 d + 2) y = 4 cos^{2} (x)

y^{^{''}} + 3 y^{^{'}} = - 48 x^{2} e^{3} x