y^{''}+5y^'-y=4x^2

Lösung

y^{^{''}} + 5 y^{^{'}} - y = 4 x^{2}

y = c_{1} e^{\frac{( - 5 + 29 ) x}{2}} + c_{2} e^{\frac{( - 5 - 29 ) x}{2}} - 4 x^{2} - 40 x - 208

Schritte zur Lösung

y^{''} (x) + 5 y^{'} (x) - y = 4 x^{2}

Solve linear ODE:

y = c_{1} e^{\frac{( - 5 + 29 ) x}{2}} + c_{2} e^{\frac{( - 5 - 29 ) x}{2}} - 4 x^{2} - 40 x - 208

y = c_{1} e^{\frac{( - 5 + 29 ) x}{2}} + c_{2} e^{\frac{( - 5 - 29 ) x}{2}} - 4 x^{2} - 40 x - 208

y^{^{''}} - 6 y^{^{'}} + 15 y = 2 sin (3 x)

y^{^{''}} - y + x = 0

D (p) = \frac{350}{p}

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

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