What is the solution for y^{''}+y=sec^3(x),y(0)=1 ?

The solution for y^{''}+y=sec^3(x),y(0)=1 is y=cos(x)+c_{2}sin(x)+(sin(x)tan(x))/2

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y^{''}+y=sec^3(x),y(0)=1

y^{^{''}} + y = sec^{3} (x), y (0) = 1

y = cos (x) + c_{2} sin (x) + \frac{sin ( x ) tan ( x )}{2}

Solution steps

y^{''} (x) + y = sec^{3} (x)

Solve linear ODE:

y = cos (x) + c_{2} sin (x) + \frac{sin ( x ) tan ( x )}{2}

y = cos (x) + c_{2} sin (x) + \frac{sin ( x ) tan ( x )}{2}

- y^{^{''}} + 10 y^{^{'}} + 25 y = 30 x + 3

y^{^{''}} + 4 y = 5 sec (2 x)

y^{^{''}} + y = e^{t} + t^{3}, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} + 4 y^{^{'}} + 4 y = 3 e^{- 2 t}

y^{^{''}} - 4 y^{^{'}} - 12 y = 3 e^{5 t}

What is the solution for y^{''}+y=sec^3(x),y(0)=1 ?
The solution for y^{''}+y=sec^3(x),y(0)=1 is y=cos(x)+c_{2}sin(x)+(sin(x)tan(x))/2