need another help. $$\frac{dy}{dx} = \frac{-(cosx.tany + cos(x+y))}{sinx.sec^2y + cos(x+y)}$$ it looks like homogeneous to me. but I get stuck in substitution of u = y/x :(

Question

lochana · Answer

is there anything with trig?

lochana · Answer

@Astrophysics @ganeshie8 can you help me

ganeshie8 · Answer

I feel there is a typo... it might be : 
$$\frac{dy}{dx} = \frac{-(cosx.tan \color{red}{y} + cos(x+y))}{sinx.sec^2y + cos(x+y)}$$

could you double check...

lochana · Answer

yes. you are right. I did a typo there

lochana · Answer

sorry about that. I didn't notice it

lochana · Answer

and this is from "Bell's mathematical series(advanced section)" book. on page 12

ganeshie8 · Answer

familiar with exact differential equations ?

lochana · Answer

no. like what?

ganeshie8 · Answer

watch this quick https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/exact-equations/v/exact-equations-example-1

ganeshie8 · Answer

$M dx + N dy = 0$


we call above differential equation is "exact" iff $M_y = N_x$

there is a special trick to solve such equations

lochana · Answer

attachment

lochana · Answer

look at 2nd one

lochana · Answer

give me a sec. I will look up exact DE

ganeshie8 · Answer

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