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Beliebt Rechnen >

4y^{''}-4y^'+y=64e^{t/2}

Lösung

4 y^{^{''}} - 4 y^{^{'}} + y = 64 e^{\frac{t}{2}}

Lösung

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{\frac{t}{2}} t + 8 e^{\frac{t}{2}} t^{2}

Schritte zur Lösung

4 y^{''} (t) - 4 y^{'} (t) + y = 64 e^{\frac{t}{2}}

Solve linear ODE:

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{\frac{t}{2}} t + 8 e^{\frac{t}{2}} t^{2}

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{\frac{t}{2}} t + 8 e^{\frac{t}{2}} t^{2}

Graph

Beliebte Beispiele

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

2y^{''}+y^'=x+sin(x)

2 y^{^{''}} + y^{^{'}} = x + sin (x)

x^{''}-4x^'+4x=e^{2t}

x^{^{''}} - 4 x^{^{'}} + 4 x = e^{2 t}

y^{''}+4y=4cos(2x)+6cos(x)+8x^2-4x

y^{^{''}} + 4 y = 4 cos (2 x) + 6 cos (x) + 8 x^{2} - 4 x

y^{''}-4y^'+3y=20cos(x)

y^{^{''}} - 4 y^{^{'}} + 3 y = 20 cos (x)