Question

Find the general solution of the given differential equation. Cos(x) dy dx (sin(x))y = 1

Answer 1

The general solution to the differential equation is y = sinx + c cosx.

What is differential equation?

It is defined as the equation which contains functions, derivative of the functions to make an expression.

We have a differential equation:

$\rm cosx\left(\dfrac{dy}{dx}\right)+\left(sinx\right)y\:=\:1$

Multiply by dx:

(cosx) dy + (sinx) y dx = dx

(cosx) dy = (1 - (sinx) y) dx

After simplification and integrating, we will get:

$\rm y = \dfrac{tan x}{sec x}+ \dfrac{c}{secx}$

y = sinx + c cosx

Thus, the general solution to the differential equation is y = sinx + c cosx.

Learn more about the differential equation here:

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