1/2 y^{''}+2y=tan(2t)-1/2 e^t

Lösung

\frac{1}{2} y^{^{''}} + 2 y = tan (2 t) - \frac{1}{2} e^{t}

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 5 cos ( 2 t ) ln ( tan ( 2 t ) + sec ( 2 t ) ) - 2 e ^{t} cos ^{2} ( 2 t ) - 2 e ^{t} sin ^{2} ( 2 t )}{10}

Schritte zur Lösung

\frac{1}{2} y^{''} (t) + 2 y = tan (2 t) - \frac{1}{2} e^{t}

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 5 cos ( 2 t ) ln ( tan ( 2 t ) + sec ( 2 t ) ) - 2 e ^{t} cos ^{2} ( 2 t ) - 2 e ^{t} sin ^{2} ( 2 t )}{10}

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 5 cos ( 2 t ) ln ( tan ( 2 t ) + sec ( 2 t ) ) - 2 e ^{t} cos ^{2} ( 2 t ) - 2 e ^{t} sin ^{2} ( 2 t )}{10}

\frac{\partial ^{2}}{\partial K ( b ) \partial b} (b L^{3} K (b) (b)^{2})

d er i v a t i v e cos^{2} (2 π x)

ma c l a u r in sin (2 x^{2})

p a r i t y x^{t a n (x)}

\frac{d}{d x} (\frac{x ^{5}}{5} - \frac{1}{2} x^{- 2})