What is the solution for y^{''}+y=sec^3(x),y(0)=2,y^'(0)= 5/2 ?

The solution for y^{''}+y=sec^3(x),y(0)=2,y^'(0)= 5/2 is y=2cos(x)+5/2 sin(x)+(sin(x)tan(x))/2

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y^{''}+y=sec^3(x),y(0)=2,y^'(0)= 5/2

y^{^{''}} + y = sec^{3} (x), y (0) = 2, y^{^{'}} (0) = \frac{5}{2}

y = 2 cos (x) + \frac{5}{2} sin (x) + \frac{sin ( x ) tan ( x )}{2}

Solution steps

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

Solve linear ODE:

y = 2 cos (x) + \frac{5}{2} sin (x) + \frac{sin ( x ) tan ( x )}{2}

y = 2 cos (x) + \frac{5}{2} sin (x) + \frac{sin ( x ) tan ( x )}{2}

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 3 y = 27 x

9 y^{^{''}} + 6 y^{^{'}} + 8 y = 37 sin (x)

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{t}}{t}

a y^{^{''}} + b y^{^{'}} + c = 0

y^{^{''}} - y^{^{'}} = \frac{e ^{x}}{( 1 + e ^{x} )}

What is the solution for y^{''}+y=sec^3(x),y(0)=2,y^'(0)= 5/2 ?
The solution for y^{''}+y=sec^3(x),y(0)=2,y^'(0)= 5/2 is y=2cos(x)+5/2 sin(x)+(sin(x)tan(x))/2