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Solve $\dfrac {d^3y}{dx^3}-6\dfrac {d^2y}{dx^2}+11\dfrac {dy}{dx}-6y=0$

written 9.5 years ago by teamques10 ★ 70k

modified 3.8 years ago by krithikkm200 • 10

Mumbai University > First Year Engineering > sem 2 > Applied Maths 2

Marks : 3

Year : 2015

engineering mathematics

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written 9.5 years ago by teamques10 ★ 70k

Auxiliary equation is

$$D^3-6D^2+11D-6=0$$

Since equating D with 1 we get

$$1-6+11-6=0$$

$(D - 1)$ is one of the factors

Now by synthetic division

$$D^2-5D+6=(D-3)(D-2)\\ (D-1)(D-3)(D-2)\\ D=1,2,3\\ Y_c=C_1e^x+C_2e^{2x}+C_3e^{3x}$$

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