- #1

Kaguro

- 221

- 57

- Homework Statement
- Solve the following differential equation:

(siny*cosy +xcos^2(y))dx + xdy=0

- Relevant Equations
- ##\frac{\partial M}{\partial y} \neq \frac{\partial N}{\partial x} ##

So equation is inexact.

Here, M = ##siny*cosy +xcos^{2}y ## and N = x

## M_y = (1/2)cos(2y) -xsin(2y)##

and ##N_x = 1##

Theorems:

If R = ## \frac{1}{N} (M_y - N_x) = f(x), then I.F. = e^{ \int f(x) dx} ##

If R = ## \frac{1}{M} (N_x - M_y) = g(y), then I.F. = e^{ \int g(x) dx} ##

Neither is holding true.

What should I do?

I tried writing N = ## x(sin^{2}y + cos^{2}y)## thinking it may help, but it didn't.

## M_y = (1/2)cos(2y) -xsin(2y)##

and ##N_x = 1##

Theorems:

If R = ## \frac{1}{N} (M_y - N_x) = f(x), then I.F. = e^{ \int f(x) dx} ##

If R = ## \frac{1}{M} (N_x - M_y) = g(y), then I.F. = e^{ \int g(x) dx} ##

Neither is holding true.

What should I do?

I tried writing N = ## x(sin^{2}y + cos^{2}y)## thinking it may help, but it didn't.