What is the solution for (D^2+1)y=csc(x) ?

The solution for (D^2+1)y=csc(x) is y=c_{1}cos(x)+c_{2}sin(x)-xcos(x)+ln(sin(x))sin(x)

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(D^2+1)y=csc(x)

(D^{2} + 1) y = csc (x)

y = c_{1} cos (x) + c_{2} sin (x) - x cos (x) + ln (sin (x)) sin (x)

Solution steps

(D^{2} + 1) y = csc (x)

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) - x cos (x) + ln (sin (x)) sin (x)

y = c_{1} cos (x) + c_{2} sin (x) - x cos (x) + ln (sin (x)) sin (x)

y^{^{''}} + 5 y^{^{'}} + 4 y = 1

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

y^{^{''}} - 4 y = e^{x}

y^{^{''}} - 4 y = - 12 e^{- 2 x} + 15 cos (x) + 8 x

y^{^{''}} + 2 y^{^{'}} + y = \frac{e ^{- x}}{1 + x ^{2}}

What is the solution for (D^2+1)y=csc(x) ?
The solution for (D^2+1)y=csc(x) is y=c_{1}cos(x)+c_{2}sin(x)-xcos(x)+ln(sin(x))sin(x)