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sameh0425

03.05.2023

Mathematics

The required value of c is -192.

Step-by-step explanation:

We are given the differential equation:

$xy'+2y=4x^2 \\(x0)$

The solution to the given differential equation is:

$y=x^2+\dfrac{c}{x^2}$

Initial condition:

y(4) = 4

Putting the values, in the solution, we get,

$4=(4)^2+\dfrac{c}{(4)^2}\\\\4 = 16+\dfrac{c}{(4)^2}\\\\\Rightarrow \dfrac{c}{(4)^2}=-12\\\Rightarrow c =-12(16)\\\Rightarrow c =-192$

Thus, the required value of c is -192.

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