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Beliebt Rechnen >

4y^{''}-4y^'+y=48e^{t/2}

Lösung

4 y^{^{''}} - 4 y^{^{'}} + y = 48 e^{\frac{t}{2}}

Lösung

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{\frac{t}{2}} t + 6 e^{\frac{t}{2}} t^{2}

Schritte zur Lösung

4 y^{''} (t) - 4 y^{'} (t) + y = 48 e^{\frac{t}{2}}

Solve linear ODE:

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{\frac{t}{2}} t + 6 e^{\frac{t}{2}} t^{2}

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{\frac{t}{2}} t + 6 e^{\frac{t}{2}} t^{2}

Graph

Beliebte Beispiele

y^{''}+3y^'+5y=sin(t),y(0)=1,y^'(0)=0

y^{^{''}} + 3 y^{^{'}} + 5 y = sin (t), y (0) = 1, y^{^{'}} (0) = 0

y^{''}+y^'-6y=3e^{2t}

y^{^{''}} + y^{^{'}} - 6 y = 3 e^{2 t}

y^{''}-4y=6x-4x^3

y^{^{''}} - 4 y = 6 x - 4 x^{3}

y^{'''}-y^{''}+4y^'-4y=-3e^t+4e^{2t}

y^{^{'''}} - y^{^{''}} + 4 y^{^{'}} - 4 y = - 3 e^{t} + 4 e^{2 t}

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

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