Question

Solve the following differential equation for a particular solution:

dy = (5x - 4y) dx; when y = 0 and x = 0.

Answer 1

Given differential equation is

dy = (5x - 4y)dx

\(\frac{dy}{dx}+4y=5x,\)

Here P = 4, Q = 5x

Now, 

I.F = \(e^{\int4\,dx}=e^{4x}\)

Solution of given equation 

When y = 0, x = 0,

∴ c = \(\frac{5}{16}\)

\(y =\frac{5}{4}x-\frac{5}{16}+\frac{5}{16}e^{-4x}\)