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

Lösung

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

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 75 cos ( 4 t ) ln ( sec ( 4 t ) + tan ( 4 t ) ) - 8 e ^{3 t} cos ^{2} ( 4 t ) - 8 e ^{3 t} sin ^{2} ( 4 t )}{150}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 75 cos ( 4 t ) ln ( sec ( 4 t ) + tan ( 4 t ) ) - 8 e ^{3 t} cos ^{2} ( 4 t ) - 8 e ^{3 t} sin ^{2} ( 4 t )}{150}

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 75 cos ( 4 t ) ln ( sec ( 4 t ) + tan ( 4 t ) ) - 8 e ^{3 t} cos ^{2} ( 4 t ) - 8 e ^{3 t} sin ^{2} ( 4 t )}{150}

\frac{d}{d x} (3 x - 8)

in v erse l a pl a ce \frac{2}{s ^{2} + 2 s + 10} \cdot \frac{1}{s}

\frac{d}{d x} (1 - (1 - \frac{x}{24})^{3})

d er i v a t i v e f (x) = (x - 5)^{6} (x + 3)^{2}

\int - 8 (y)^{2} (1) d y