Solve the differential equation $\dfrac{{dy}}{{dx}} + y\tan x = {\cos ^3}x$ If the HCF of \[408\] and $1032$ is expressible in the form $1032m - 408 \times 5$, find $m$

Question

Solve the differential equation  $\dfrac{{dy}}{{dx}} + y\tan x = {\cos ^3}x$ If the HCF of $$408$$ and $1032$ is expressible in the form   $1032m - 408 \times 5$, find $m$

Vedantu Content Team · Accepted Answer

Hint: Here we find the HCF of given numbers by using Euclid’s division Algorithm
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By using Euclid’s Division Algorithm lets us find the HCF of given numbers
Euclid’s Division Algorithm:
    Dividend =divisor$ \times $quotient$ + $remainder
Here larger number will be the dividend and smaller number will be the divisor
    $1032 = 408 \times 2 + 216$
    $408 = 216 \times 1 + 192$
    $216 = 192 \times 1 + 24$
     $192 = 24 \times 8 + 0$
Since here the remainder is $0$ Therefore HCF of $1032$ and$408$ is $24$
Now let us equate the given form with HCF of given numbers
$1032m - 408 \times 5$=$24$
$1032m = 2064$
$m = 2$
So here value of $m = 2$

NOTE: We can also find the HCF of two numbers by division method by dividing the larger number with the smaller number.

Solve the differential equation $\dfrac{{dy}}{{dx}} + y\tan x = {\cos ^3}x$ If the HCF of \[408\] and $1032$ is expressible in the form $1032m - 408 \times 5$, find $m$

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Solve the differential equation $\dfrac{{dy}}{{dx}} + y\tan x = {\cos ^3}x$ If the HCF of \[408\] and $1032$ is expressible in the form $1032m - 408 \times 5$, find $m$

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