What is the solution for y^{''}+y=csc^2(t) ?

The solution for y^{''}+y=csc^2(t) is y=c_{1}cos(t)+c_{2}sin(t)-cos(t)ln(tan(t/2))-1

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y^{''}+y=csc^2(t)

y^{^{''}} + y = csc^{2} (t)

y = c_{1} cos (t) + c_{2} sin (t) - cos (t) ln (tan (\frac{t}{2})) - 1

Solution steps

y^{''} (t) + y = csc^{2} (t)

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t) - cos (t) ln (tan (\frac{t}{2})) - 1

y = c_{1} cos (t) + c_{2} sin (t) - cos (t) ln (tan (\frac{t}{2})) - 1

(1.4) (5.7)

\int_{- 1}^{1} (x^{2} - 2) d x

x \to 0 lim (\frac{sin ( x ^{4} )}{x})

10

\int_{1}^{\infty} \frac{2}{x ^{2} + 1} d x

What is the solution for y^{''}+y=csc^2(t) ?
The solution for y^{''}+y=csc^2(t) is y=c_{1}cos(t)+c_{2}sin(t)-cos(t)ln(tan(t/2))-1