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Beliebt Rechnen >

(d^2y)/(dx^2)+8(dy)/(dx)+25y=16sin(x)

Lösung

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 25 y = 16 sin (x)

Lösung

y = e^{- 4 x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{3}{5} sin (x) - \frac{1}{5} cos (x)

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 25 y = 16 sin (x)

Solve linear ODE:

y = e^{- 4 x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{3}{5} sin (x) - \frac{1}{5} cos (x)

y = e^{- 4 x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{3}{5} sin (x) - \frac{1}{5} cos (x)

Graph

Beliebte Beispiele

y^{''''}-y=cos(x)

y^{^{''''}} - y = cos (x)

y^{''}-y^'-2y=2x+2

y^{^{''}} - y^{^{'}} - 2 y = 2 x + 2

y^{''}+10y^'+9y=6cos(3t+1.5708)\H(t)

y^{^{''}} + 10 y^{^{'}} + 9 y = 6 cos (3 t + 1.5708) H (t)

(d^2y)/(dx^2)+4y=tan(2x)

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

y^{''''}+2y^{''}+1=0

y^{^{''''}} + 2 y^{^{''}} + 1 = 0