Question

the solution of differential equation 25r-40s+16t=0 is

Answer 1

yeah sure for your help

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Thanks !

Here is your answer which you are searching for

The given differential equation is

( $D^{2}$ + 4 DD' - $5D'^{2}$ )Z = 0

Auxiliary equation is

$25m^{2} - 40 m+16 = 0$

$( 5m - 4)^{2}$ = 0

m = $\frac{4}{5} ,\frac{4}{5}$

$C.f. = f_{1 ( y +\frac{4}{5} x) +xf_{2} ( y +\frac{4}{5} x)$

===> P.I. =0

The complete solution of that is

z = c.f. + p. I .

===> $f_{1 ( y +\frac{4}{5} x) +xf_{2} ( y +\frac{4}{5} x)$

===> $f_{1} ( 5y +4x) + xf_{2} (5y +4x)$

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