What is the solution for 3x^{''}+2x^'+3x=0 ?

The solution for 3x^{''}+2x^'+3x=0 is x=e^{-t/3}(c_{1}cos((2^{3/2}t)/3)+c_{2}sin((2^{3/2}t)/3))

Popular >

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

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

x = e^{- \frac{t}{3}} (c_{1} cos (\frac{2 ^{\frac{3}{2}} t}{3}) + c_{2} sin (\frac{2 ^{\frac{3}{2}} t}{3}))

Solution steps

3 x^{''} (t) + 2 x^{'} (t) + 3 x = 0

Solve linear ODE:

x = e^{- \frac{t}{3}} (c_{1} cos (\frac{2 ^{\frac{3}{2}} t}{3}) + c_{2} sin (\frac{2 ^{\frac{3}{2}} t}{3}))

x = e^{- \frac{t}{3}} (c_{1} cos (\frac{2 ^{\frac{3}{2}} t}{3}) + c_{2} sin (\frac{2 ^{\frac{3}{2}} t}{3}))

4 y^{^{''}} + 12 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = - 4

y^{^{''}} + 5 y^{^{'}} = 0, y (0) = 5, y^{^{'}} (0) = - 20

y^{^{''}} + 4 y^{^{'}} + 7 y = 0, y (0) = 1, y^{^{'}} (0) = - 2

y^{^{''}} - 2 y^{^{'}} - 3 y = 0, y (0) = 0, y^{^{'}} (0) = - 4

y^{^{''}} + 81 y = 0, y (0) = 0, y^{^{'}} (0) = 3

What is the solution for 3x^{''}+2x^'+3x=0 ?
The solution for 3x^{''}+2x^'+3x=0 is x=e^{-t/3}(c_{1}cos((2^{3/2}t)/3)+c_{2}sin((2^{3/2}t)/3))