What is the solution for y^{''}+0.01(20-y)=0 ?

The solution for y^{''}+0.01(20-y)=0 is y=c_{1}e^{t/(10)}+c_{2}e^{-t/(10)}+20

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y^{''}+0.01(20-y)=0

y^{^{''}} + 0.01 (20 - y) = 0

y = c_{1} e^{\frac{t}{10}} + c_{2} e^{- \frac{t}{10}} + 20

Solution steps

y^{''} (t) + 0.01 (20 - y) = 0

Solve linear ODE:

y = c_{1} e^{\frac{t}{10}} + c_{2} e^{- \frac{t}{10}} + 20

y = c_{1} e^{\frac{t}{10}} + c_{2} e^{- \frac{t}{10}} + 20

y^{^{''}} + 4 y^{^{'}} + 4 y = 3 x + 7

y^{^{''}} - 2 y^{^{'}} + y = 4 x^{2} - 3

\frac{1}{2} y^{^{''}} + \frac{1}{2} y^{^{'}} + 6 y = 10 cos (3 x)

y^{^{''}} + \frac{750}{30} y = \frac{20}{30} cos (2) t

5 y^{^{''}} + 180 y = 150 sin (3 t)

What is the solution for y^{''}+0.01(20-y)=0 ?
The solution for y^{''}+0.01(20-y)=0 is y=c_{1}e^{t/(10)}+c_{2}e^{-t/(10)}+20