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

解答

y^{^{''}} + 3 \cdot y^{^{'}} + 2 \cdot y = x

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{1}{2} x - \frac{π}{2} e^{- x} erfi (x) + \frac{2 π}{8} e^{- 2 x} erfi (2 x)

求解步骤

y^{''} (x) + 3 \cdot y^{'} (x) + 2 \cdot y = x

求解线性方程:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{1}{2} x - \frac{π}{2} e^{- x} erfi (x) + \frac{2 π}{8} e^{- 2 x} erfi (2 x)

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{1}{2} x - \frac{π}{2} e^{- x} erfi (x) + \frac{2 π}{8} e^{- 2 x} erfi (2 x)

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

\frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} + x = 1, x (0) = 0

y^{^{''}} - y^{^{'}} + y = 14 sin (t)

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 14 y = (x + 1) e^{x}

y^{^{''}} - 7 y^{^{'}} + 12 y = sin (x) - cos (x)