What is the solution for 60x^{''}+240x=0,x(0)=0,x^'(0)=-8 ?

The solution for 60x^{''}+240x=0,x(0)=0,x^'(0)=-8 is x=-4sin(2t)

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60x^{''}+240x=0,x(0)=0,x^'(0)=-8

60 x^{^{''}} + 240 x = 0, x (0) = 0, x^{^{'}} (0) = - 8

x = - 4 sin (2 t)

Solution steps

60 x^{''} (t) + 240 x = 0

Solve linear ODE:

x = - 4 sin (2 t)

x = - 4 sin (2 t)

4 y^{^{''}} + 9 y^{^{'}} + 9 y = 0

y^{^{''}} - 10 y^{^{'}} - 144 y = 0, y (0) = 9, y^{^{'}} (0) = 58

y^{^{''}} + a \cdot y^{^{'}} - b \cdot y = 0

y^{^{''}} - 10 y^{^{'}} + 6 y = 0

y^{^{''}} + 8 y^{^{'}} + 41 y = 0, y (0) = 3, y^{^{'}} (0) = - 8

What is the solution for 60x^{''}+240x=0,x(0)=0,x^'(0)=-8 ?
The solution for 60x^{''}+240x=0,x(0)=0,x^'(0)=-8 is x=-4sin(2t)