(d^2y)/(dx^2)+4(dy)/(dx)+5y=2sin(x)

Lösung

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 5 y = 2 sin (x)

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{1}{4} sin (x) - \frac{1}{4} cos (x)

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 5 y = 2 sin (x)

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{1}{4} sin (x) - \frac{1}{4} cos (x)

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{1}{4} sin (x) - \frac{1}{4} cos (x)

\frac{\partial}{\partial x} (2 x yz)

d er i v a t i v e y = \frac{3 x}{x}

\int \frac{ln ^{6} ( x )}{x} d x

x \to 0 lim (\frac{3 sin ( x ) + x}{x})

\int \frac{1}{3 x ( 5 + x )} d x