Mister Exam

Differential equation y’’’-6y’’+11y’-6y=0

For Cauchy problem:

y() =
y'() =
y''() =
y'''() =
y''''() =

The graph:

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The solution

You have entered [src]
      2                                  3          
     d                      d           d           
- 6*---(y(x)) - 6*y(x) + 11*--(y(x)) + ---(y(x)) = 0
      2                     dx           3          
    dx                                 dx           
$$- 6 y{\left(x \right)} + 11 \frac{d}{d x} y{\left(x \right)} - 6 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$$
-6*y + 11*y' - 6*y'' + y''' = 0
The answer [src]
       /         x       2*x\  x
y(x) = \C1 + C2*e  + C3*e   /*e 
$$y{\left(x \right)} = \left(C_{1} + C_{2} e^{x} + C_{3} e^{2 x}\right) e^{x}$$
The classification
nth linear constant coeff homogeneous
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