2y^{''}+y^'=3x^2+10x

解答

2 y^{^{''}} + y^{^{'}} = 3 x^{2} + 10 x

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

求解步骤

2 y^{''} (x) + y^{'} (x) = 3 x^{2} + 10 x

求解线性方程:

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

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

3 y^{^{''}} + 2 (9.81)^{2} y = 49 (9.81) cos (8 t)

y^{^{''}} - 4 y^{^{'}} = 2 x - 1

y^{^{'''}} + 2 y^{^{''}} - 9 y^{^{'}} - 18 = 10 + 20 sin (5 t)

y^{^{''}} + y^{^{'}} - 6 y = x + e^{2 x}

y^{^{''}} + 12 y^{^{'}} + 100 y = 6