Question

the particular integral of the differential equation
$(d^{2} - 5d + 6)y - 24)$
is​

Answer 1

Answer:

A linear differential equation is that in which the dependent variable and its derivatives occur ... Example 2: Solve (D2 – 5D + 6) y = cos 3x.

Answer 2

SOLUTION

TO DETERMINE

The particular integral of the differential equation

$\displaystyle \sf{( {D}^{2} - 5D + 6)y = 24 }$

EVALUATION

Here the given differential equation is

$\displaystyle \sf{( {D}^{2} - 5D + 6)y = 24 }$

Now the required particular integral is given by

$\displaystyle \sf{ P.I.= \frac{1}{ {D}^{2} - 5D + 6} \: \: .24 }$

$\displaystyle \sf{ =24. \: \: \frac{1}{ {D}^{2} - 5D + 6} \: \: 1 }$

$\displaystyle \sf{ =24. \: \: \frac{1}{ {D}^{2} - 5D + 6} \: \: {e}^{0x} }$

$\displaystyle \sf{ =24. \: \: \frac{1}{ {0}^{2} - 5 \times 0 + 6} \: \: {e}^{0x} }$

$\displaystyle \sf{ =24. \: \: \frac{1}{6} \: \times \: 1 }$

$\displaystyle \sf{ =4 }$

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