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Beliebt Rechnen >

linear y^{''}+y^'-2y=upi(t)-u^2pi(t)

Lösung

linear

y^{^{''}} + y^{^{'}} - 2 y = u π (t) - u^{2} π (t)

Lösung

y = c_{1} e^{t} + c_{2} e^{- 2 t} - \frac{t ( π u - π u ^{2} )}{2} - \frac{π u - π u ^{2}}{4}

Schritte zur Lösung

y^{''} (t) + y^{'} (t) - 2 y = u π (t) - u^{2} π (t)

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{- 2 t} - \frac{t ( π u - π u ^{2} )}{2} - \frac{π u - π u ^{2}}{4}

y = c_{1} e^{t} + c_{2} e^{- 2 t} - \frac{t ( π u - π u ^{2} )}{2} - \frac{π u - π u ^{2}}{4}

Graph

Beliebte Beispiele

y^{''}+2y^'+2y=5

y^{^{''}} + 2 y^{^{'}} + 2 y = 5

y^{''}-4y^'-5y=6x^2+4x+1

y^{^{''}} - 4 y^{^{'}} - 5 y = 6 x^{2} + 4 x + 1

y^{''}+2y^'+2y=4

y^{^{''}} + 2 y^{^{'}} + 2 y = 4

y^{''}-6y^'+9y=5t^2,y(0)=0,y^'(0)=1

y^{^{''}} - 6 y^{^{'}} + 9 y = 5 t^{2}, y (0) = 0, y^{^{'}} (0) = 1

y^{''}-8y^'+16y=16x+7

y^{^{''}} - 8 y^{^{'}} + 16 y = 16 x + 7