What is the solution for x^{''}+16x=0,x(0)=-1,x^'(0)=-5 ?

The solution for x^{''}+16x=0,x(0)=-1,x^'(0)=-5 is x=-cos(4t)-5/4 sin(4t)

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x^{''}+16x=0,x(0)=-1,x^'(0)=-5

x^{^{''}} + 16 x = 0, x (0) = - 1, x^{^{'}} (0) = - 5

x = - cos (4 t) - \frac{5}{4} sin (4 t)

Solution steps

x^{''} (t) + 16 x = 0

Solve linear ODE:

x = - cos (4 t) - \frac{5}{4} sin (4 t)

x = - cos (4 t) - \frac{5}{4} sin (4 t)

What is the solution for x^{''}+16x=0,x(0)=-1,x^'(0)=-5 ?
The solution for x^{''}+16x=0,x(0)=-1,x^'(0)=-5 is x=-cos(4t)-5/4 sin(4t)