What is the solution for 3x^{''}+75x=0,x(0)=0,x^'(0)=-10 ?

The solution for 3x^{''}+75x=0,x(0)=0,x^'(0)=-10 is x=-2sin(5t)

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3x^{''}+75x=0,x(0)=0,x^'(0)=-10

3 x^{^{''}} + 75 x = 0, x (0) = 0, x^{^{'}} (0) = - 10

x = - 2 sin (5 t)

Solution steps

3 x^{''} (t) + 75 x = 0

Solve linear ODE:

x = - 2 sin (5 t)

x = - 2 sin (5 t)

12 y^{^{''}} - 13 y^{^{'}} + y = 0, y (0) = 12, y^{^{'}} (0) = \frac{1}{12}

16 y^{^{''}} + 12 y^{^{'}} + 9 y = 0

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

(D^{2} - 9 D + 18) y = 0

16 y^{^{''}} = - 49 y^{^{'}}

What is the solution for 3x^{''}+75x=0,x(0)=0,x^'(0)=-10 ?
The solution for 3x^{''}+75x=0,x(0)=0,x^'(0)=-10 is x=-2sin(5t)