What is the solution for x^{''}+7x^'+10x=20,x(0)=5,x^'(0)=3 ?

The solution for x^{''}+7x^'+10x=20,x(0)=5,x^'(0)=3 is x=6e^{-2t}-3e^{-5t}+2

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x^{''}+7x^'+10x=20,x(0)=5,x^'(0)=3

x^{^{''}} + 7 x^{^{'}} + 10 x = 20, x (0) = 5, x^{^{'}} (0) = 3

x = 6 e^{- 2 t} - 3 e^{- 5 t} + 2

Solution steps

x^{''} (t) + 7 x^{'} (t) + 10 x = 20

Solve linear ODE:

x = 6 e^{- 2 t} - 3 e^{- 5 t} + 2

x = 6 e^{- 2 t} - 3 e^{- 5 t} + 2

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 x^{2} + 1

y^{^{''}} + 2 y^{^{'}} + y = e^{- x} sin (x)

\frac{d ^{2} x}{d t ^{2}} + 16 x = 1 + 2 sin (4 t)

y^{^{''}} - 4 y = 2 x - sin (x)

y^{^{''}} + y^{^{'}} - 2 y = 5

What is the solution for x^{''}+7x^'+10x=20,x(0)=5,x^'(0)=3 ?
The solution for x^{''}+7x^'+10x=20,x(0)=5,x^'(0)=3 is x=6e^{-2t}-3e^{-5t}+2