(d^2y)/(dx^2)-4(dy)/(dx)+13y=8sin(3x),y(0)=1,y^'(0)=2

Lösung

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 13 y = 8 sin (3 x), y (0) = 1, y^{^{'}} (0) = 2

y = e^{2 x} (\frac{2}{5} cos (3 x) + \frac{1}{5} sin (3 x)) + \frac{1}{5} sin (3 x) + \frac{3}{5} cos (3 x)

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) + 13 y = 8 sin (3 x)

Solve linear ODE:

y = e^{2 x} (\frac{2}{5} cos (3 x) + \frac{1}{5} sin (3 x)) + \frac{1}{5} sin (3 x) + \frac{3}{5} cos (3 x)

y = e^{2 x} (\frac{2}{5} cos (3 x) + \frac{1}{5} sin (3 x)) + \frac{1}{5} sin (3 x) + \frac{3}{5} cos (3 x)

x \to 1 lim ((9 x^{2}) + 30 x + 25)

l a pl a ce t r an s f or m 4 y

\int x^{25} sin (x^{26}) d x

d er i v a t i v e e^{5}

\frac{\partial}{\partial x} (y^{2} sin (\frac{x}{y}))