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Beliebt Rechnen >

y^{''}-5y^'+6y=2te^{2t},y^'(0)=-3

Lösung

y^{^{''}} - 5 y^{^{'}} + 6 y = 2 t e^{2 t}, y^{^{'}} (0) = - 3

Lösung

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

Schritte zur Lösung

y^{''} (t) - 5 y^{'} (t) + 6 y = 2 t e^{2 t}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''''}+y=cos(x)

y^{^{''''}} + y = cos (x)

y^{''}-4y^'+5y=4e^{3t},y(0)=2,y^'(0)=7

y^{^{''}} - 4 y^{^{'}} + 5 y = 4 e^{3 t}, y (0) = 2, y^{^{'}} (0) = 7

y^{'''}-2y^{''}-5y^'+6y=e^x+x^2

y^{^{'''}} - 2 y^{^{''}} - 5 y^{^{'}} + 6 y = e^{x} + x^{2}

x^{''}+3x^'+2x=sin(3t)

x^{^{''}} + 3 x^{^{'}} + 2 x = sin (3 t)

x^{''}+8x^'+16=0

x^{^{''}} + 8 x^{^{'}} + 16 = 0