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Beliebt Rechnen >

(d^2y)/(dx^2)-4(dy)/(dx)-12=3cos(x)

Lösung

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 12 = 3 cos (x)

Lösung

y = c_{1} e^{4 x} + c_{2} - \frac{12}{17} sin (x) - \frac{3}{17} cos (x) - 3 x

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 12 = 3 cos (x)

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} - \frac{12}{17} sin (x) - \frac{3}{17} cos (x) - 3 x

y = c_{1} e^{4 x} + c_{2} - \frac{12}{17} sin (x) - \frac{3}{17} cos (x) - 3 x

Graph

Beliebte Beispiele

y^{^{''}} + 4 y = - 1

y^{''}-3y^'+2y=(e^{2x})/(1+e^{2x)}

y^{^{''}} - 3 y^{^{'}} + 2 y = \frac{e ^{2 x}}{1 + e ^{2 x}}

(d^2-2d+2)y=4x-2+2e^xsin(x)

(d^{2} - 2 d + 2) y = 4 x - 2 + 2 e^{x} sin (x)

y^{''}-2y^'=30e^{-3t},y(0)=1,y^'(0)=0

y^{^{''}} - 2 y^{^{'}} = 30 e^{- 3 t}, y (0) = 1, y^{^{'}} (0) = 0

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

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