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Beliebt Rechnen >

y^{''}-a^2y=-2sin(pix)-4sin(3pi*x)

Lösung

y^{^{''}} - a^{2} y = - 2 sin (π \cdot x) - 4 sin (3 \cdot π \cdot x)

Lösung

y = c_{1} e^{a x} + c_{2} e^{- a x} + \frac{2 sin ( π x )}{a ^{2} + π ^{2}} + \frac{4 sin ( 3 π x )}{a ^{2} + 9 π ^{2}}

Schritte zur Lösung

y^{''} (x) - a^{2} y = - 2 sin (π \cdot x) - 4 sin (3 \cdot π \cdot x)

Solve linear ODE:

y = c_{1} e^{a x} + c_{2} e^{- a x} + \frac{2 sin ( π x )}{a ^{2} + π ^{2}} + \frac{4 sin ( 3 π x )}{a ^{2} + 9 π ^{2}}

y = c_{1} e^{a x} + c_{2} e^{- a x} + \frac{2 sin ( π x )}{a ^{2} + π ^{2}} + \frac{4 sin ( 3 π x )}{a ^{2} + 9 π ^{2}}

Graph

Beliebte Beispiele

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

y^{''}+7/2 y^'+3/2 y=2e^{-3x}

y^{^{''}} + \frac{7}{2} y^{^{'}} + \frac{3}{2} y = 2 e^{- 3 x}

y^{''}+4^2y=cos(2t)

y^{^{''}} + 4^{2} y = cos (2 t)

y^{''}-10y^'+21y=192e^t

y^{^{''}} - 10 y^{^{'}} + 21 y = 192 e^{t}

y^{^{''}} + y = - 3 x - 2