y^{''}+3/2 y^'=x+e^{2x}

解答

y^{^{''}} + \frac{3}{2} y^{^{'}} = x + e^{2 x}

y = c_{1} + c_{2} e^{- \frac{3 x}{2}} + \frac{x ^{2}}{3} - \frac{4 x}{9} + \frac{1}{7} e^{2 x}

求解步骤

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

求解线性方程:

y = c_{1} + c_{2} e^{- \frac{3 x}{2}} + \frac{x ^{2}}{3} - \frac{4 x}{9} + \frac{1}{7} e^{2 x}

y = c_{1} + c_{2} e^{- \frac{3 x}{2}} + \frac{x ^{2}}{3} - \frac{4 x}{9} + \frac{1}{7} e^{2 x}

\frac{d ^{4} y}{d x ^{4}} + 6 \frac{d y}{d x} = - 5 x^{2}

y^{^{''}} + y^{^{'}} - 8 y = 9 e^{3 t}

y^{^{''}} + 2 y^{^{'}} + y = 18 e^{2 x} - 4 sin (x) - x^{2}

3 y^{^{''}} - 2 y - y = 2 t^{2} - t - 3 e^{- 3 t}

y^{^{''}} - 2 y^{^{'}} - 15 y = (6 t + 3 tt + 1) e^{t}