y^{''}+y=cot^2(x)

Lösung

y^{^{''}} + y = cot^{2} (x)

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

Schritte zur Lösung

y^{''} (x) + y = cot^{2} (x)

Solve linear ODE:

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

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

in v erse l a pl a ce \frac{( s + 4 )}{( s ^{2} - 2 s + 4 )}

(- 16 x y^{2} + 3 y) + (- 16 x^{2} y + 3 x) y^{^{'}} = 0

t an g e n t x^{2} + x y + 2 y^{2} = 18, (3, - 3)

\int \frac{x}{x ^{2} + 6 x + 13} d x

\int x e^{- x} sin (x) d x