Question

The non separable differential equation dy dx = 8x − 2y has a linear particular solution of the form y = mx + b. Find m + b.

Answer 1

Answer:

$m + b=2$

Step-by-step explanation:

From the question we are told that

The non separable differential equation $\frac{dy}{dx} = 8x - 2y$

Generally the chi form of a give equation is mathematically represented as

$\frac{dy}{dx} +P(x)y= q(x)$

$\frac{dy}{dx} + 2y = 8x$

$ye^2^x=\int e^2^.8xdxx$

$ye^2^x=8(\frac{xe^2^x}{2}-\frac{\int e^2^x}{2})$

$ye^2^x=8(\frac{xe^2^x}{2}-\frac{e^2^x}{1})+c$

$ye^2^x=4x^2^x-2e^2^x+c$

$y=4x-2+c$

for c=0

$y=4x-2$

Therefore

$m=4\\b=-2\\m + b=4-(+2)$

$m + b=2$