y^{''}+y=0,y(0)=2,y^'(0)=3

解答

y^{^{''}} + y = 0, y (0) = 2, y^{^{'}} (0) = 3

y = 2 cos (t) + 3 sin (t)

求解步骤

y^{''} (t) + y = 0

求解线性方程:

y = 2 cos (t) + 3 sin (t)

y = 2 cos (t) + 3 sin (t)

4 \frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + y = 0

41 y - 8 y^{^{'}} + y^{^{''}} = 0, y (0) = - 3, y^{^{'}} (0) = - 32

\frac{y ^{^{''}} + y ^{^{'}}}{y} = 0

- y^{^{''}} - y = 0

y^{^{''}} + 25 y = 0, y (0) = 0, y^{^{'}} (0) = 20