What is the solution for 10x^{''}+1/90 x=0,x(0)=100,x^'(0)=25 ?

The solution for 10x^{''}+1/90 x=0,x(0)=100,x^'(0)=25 is x=100cos(t/(30))+750sin(t/(30))

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10x^{''}+1/90 x=0,x(0)=100,x^'(0)=25

10 x^{^{''}} + \frac{1}{90} x = 0, x (0) = 100, x^{^{'}} (0) = 25

x = 100 cos (\frac{t}{30}) + 750 sin (\frac{t}{30})

Solution steps

10 x^{''} (t) + \frac{1}{90} x = 0

Solve linear ODE:

x = 100 cos (\frac{t}{30}) + 750 sin (\frac{t}{30})

x = 100 cos (\frac{t}{30}) + 750 sin (\frac{t}{30})

\frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 8 y = 0

6 y^{^{''}} + 35 y = 0, y (0) = 3, y^{^{'}} (0) = 8

16 y^{^{''''}} = y

3 y^{^{''}} + 10 y^{^{'}} - 8 y = 0

y^{^{'''}} + 4 y^{^{''}} - 128 y = 0

What is the solution for 10x^{''}+1/90 x=0,x(0)=100,x^'(0)=25 ?
The solution for 10x^{''}+1/90 x=0,x(0)=100,x^'(0)=25 is x=100cos(t/(30))+750sin(t/(30))