u^{''}-a*\H(x)=x,u^'(-1)=0,u^'(1)=0

解答

u^{^{''}} - a \cdot H (x) = x, u^{^{'}} (- 1) = 0, u^{^{'}} (1) = 0

u (x) = \int \int x + a H (x) d x d x

求解步骤

u^{''} (x) - a \cdot H (x) = x

整理

u^{''} (x) : u^{''} (x) = x + a H (x)

解

u^{''} (x) = x + a H (x) : u^{'} (x) = \int x + a H (x) d x

解

u^{'} (x) = \int x + a H (x) d x : u (x) = \int \int x + a H (x) d x d x

u (x) = \int \int x + a H (x) d x d x

y^{^{''}} + 4 y = e^{3 t}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + a^{2} y = cos (b t)

y^{^{''}} - 12 y^{^{'}} + 36 y = 7 + 2 x

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

y^{^{''}} - 3 y = cos (3 x)