What is the solution for y^{''}+14y^'+50y=0,y(0)=-5,y^'(0)=5 ?

The solution for y^{''}+14y^'+50y=0,y(0)=-5,y^'(0)=5 is y=e^{-7t}(-5cos(t)-30sin(t))

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y^{''}+14y^'+50y=0,y(0)=-5,y^'(0)=5

y^{^{''}} + 14 y^{^{'}} + 50 y = 0, y (0) = - 5, y^{^{'}} (0) = 5

y = e^{- 7 t} (- 5 cos (t) - 30 sin (t))

Solution steps

y^{''} (t) + 14 y^{'} (t) + 50 y = 0

Solve linear ODE:

y = e^{- 7 t} (- 5 cos (t) - 30 sin (t))

y = e^{- 7 t} (- 5 cos (t) - 30 sin (t))

v^{^{''}} + 3 v^{^{'}} + 2 v = 0

y^{^{''}} + 43 y^{^{'}} + 8 y = 0

y^{^{''}} + k y^{^{'}} - 2 k^{2} y = 0

y^{^{''}} - 2 y^{^{'}} + y = 0, y (0) = 9, y (1) = 5

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = 2, y^{^{'}} (0) = - 13

What is the solution for y^{''}+14y^'+50y=0,y(0)=-5,y^'(0)=5 ?
The solution for y^{''}+14y^'+50y=0,y(0)=-5,y^'(0)=5 is y=e^{-7t}(-5cos(t)-30sin(t))