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Beliebt Rechnen >

4y^{''}-4y^'+y=24e^{t/2}

Lösung

4 y^{^{''}} - 4 y^{^{'}} + y = 24 e^{\frac{t}{2}}

Lösung

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{\frac{t}{2}} t + 3 e^{\frac{t}{2}} t^{2}

Schritte zur Lösung

4 y^{''} (t) - 4 y^{'} (t) + y = 24 e^{\frac{t}{2}}

Solve linear ODE:

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{\frac{t}{2}} t + 3 e^{\frac{t}{2}} t^{2}

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{\frac{t}{2}} t + 3 e^{\frac{t}{2}} t^{2}

Graph

Beliebte Beispiele

y^{''''}+36y^{''}=sin(6t)+te^{7t}+4

y^{^{''''}} + 36 y^{^{''}} = sin (6 t) + t e^{7 t} + 4

y^{''}+8y=16sin(x)

y^{^{''}} + 8 y = 16 sin (x)

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

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

y^{'''}-2y^{''}+2y^'=cos(x)+e^x

y^{^{'''}} - 2 y^{^{''}} + 2 y^{^{'}} = cos (x) + e^{x}

y^{''}+4y^'+8y=sin(x)

y^{^{''}} + 4 y^{^{'}} + 8 y = sin (x)