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Beliebt Rechnen >

y^{''}+y^'-y=t*e^t

Lösung

y^{^{''}} + y^{^{'}} - y = t \cdot e^{t}

Lösung

y = c_{1} e^{\frac{( - 1 + 5 ) t}{2}} + c_{2} e^{\frac{( - 1 - 5 ) t}{2}} + e^{t} t - 3 e^{t}

Schritte zur Lösung

y^{''} (t) + y^{'} (t) - y = t \cdot e^{t}

Solve linear ODE:

y = c_{1} e^{\frac{( - 1 + 5 ) t}{2}} + c_{2} e^{\frac{( - 1 - 5 ) t}{2}} + e^{t} t - 3 e^{t}

y = c_{1} e^{\frac{( - 1 + 5 ) t}{2}} + c_{2} e^{\frac{( - 1 - 5 ) t}{2}} + e^{t} t - 3 e^{t}

Graph

Beliebte Beispiele

x^{''}+12x^'+11x=9cos(2t)

x^{^{''}} + 12 x^{^{'}} + 11 x = 9 cos (2 t)

y^{''}-7y^'=5x*e^x

y^{^{''}} - 7 y^{^{'}} = 5 x \cdot e^{x}

y^{''}+y^'-32y=16cos(x)

y^{^{''}} + y^{^{'}} - 32 y = 16 cos (x)

y^{''}+4y=32sin(4t),y(0)=1

y^{^{''}} + 4 y = 32 sin (4 t), y (0) = 1

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

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