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Beliebt Rechnen >

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

Lösung

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^{''}+4y^'+3y=-19te^{3t}

y^{^{''}} + 4 y^{^{'}} + 3 y = - 19 t e^{3 t}

y^{''}+4y^'=sin(t)

y^{^{''}} + 4 y^{^{'}} = sin (t)

y^{''}-5y^'+6y=-5e^{3x}

y^{^{''}} - 5 y^{^{'}} + 6 y = - 5 e^{3 x}

y^{''}-2y^'+y=t^2+1

y^{^{''}} - 2 y^{^{'}} + y = t^{2} + 1

y^{''}+8y^'+16y=6cos(4t)

y^{^{''}} + 8 y^{^{'}} + 16 y = 6 cos (4 t)