Question

y is equals to x /p - ap where p= dy/dx​

Answer 1

Answer:

\huge\red{Answer}Answer

We have,y = (1+p)x + ap2 ....(1)

differentiating with respect to x, we get

dy/dx = 1 + p + x dp/dx + 2ap dp/ᴅx

⇒p = 1+p+x dp/dx + 2ap dp/ᴅx

⇒dx/dp + x = −2ap

The above is a linear differential equation.

Now, IF = e∫dp = ep

Now, the solution of the differential equation is :

xe^p = ∫−2ap×e^p dp + ᴄ

⇒xe^p = −2a[pe^p−e^p] + ᴄ

⇒xe^p = −2ape^p + 2ae^p + ᴄ

⇒x = −2ap + 2a + Ce−p ......(2)

Now, putting the value of x in (1), we ɢᴇᴛ

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ʜᴏᴩᴇ ɪᴛ ʜᴇʟᴩꜱ ᴜ !!