1/4 y^{''}+4y=tan(4t)-1/2 e^{3t}

Lösung

\frac{1}{4} y^{^{''}} + 4 y = tan (4 t) - \frac{1}{2} e^{3 t}

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 25 cos ( 4 t ) ln ( tan ( 4 t ) + sec ( 4 t ) ) - 8 e ^{3 t} cos ^{2} ( 4 t ) - 8 e ^{3 t} sin ^{2} ( 4 t )}{100}

Schritte zur Lösung

\frac{1}{4} y^{''} (t) + 4 y = tan (4 t) - \frac{1}{2} e^{3 t}

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 25 cos ( 4 t ) ln ( tan ( 4 t ) + sec ( 4 t ) ) - 8 e ^{3 t} cos ^{2} ( 4 t ) - 8 e ^{3 t} sin ^{2} ( 4 t )}{100}

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 25 cos ( 4 t ) ln ( tan ( 4 t ) + sec ( 4 t ) ) - 8 e ^{3 t} cos ^{2} ( 4 t ) - 8 e ^{3 t} sin ^{2} ( 4 t )}{100}

x \to 0 lim (\frac{1 1 ^{x} - 1 0 ^{x}}{x})

d er i v a t i v e G (t) = \frac{4 t}{t + 5}

\frac{d}{d x} (arcsin (3 x - 4 x^{3}))

d er i v a t i v e lo g_{3} (11) p^{3}

t an g e n t y = \frac{5}{x}, (1, 5)