y^{''}+y=x^2+1,y(0)=5,y(1)=0

解答

y^{^{''}} + y = x^{2} + 1, y (0) = 5, y (1) = 0

y = 6 cos (x) - \frac{6 cos ( 1 ) sin ( x )}{sin ( 1 )} + x^{2} - 1

求解步骤

y^{''} (x) + y = x^{2} + 1

求解线性方程:

y = 6 cos (x) - \frac{6 cos ( 1 ) sin ( x )}{sin ( 1 )} + x^{2} - 1

y = 6 cos (x) - \frac{6 cos ( 1 ) sin ( x )}{sin ( 1 )} + x^{2} - 1

y^{^{''}} + 25 y = 10 sin (5 t)

y^{^{''}} - 12 y^{^{'}} + 36 y = 12 x + 6

x^{^{''}} + 100 x^{^{'}} + 2500 x = 30

(D^{3} + D^{2} - 4 D - 4) y = 3 e^{- x} - 4 x - 6

y^{^{''}} + 2 y^{^{'}} + 5 y = 30 x^{3} + 2