Question

find a set of solutions,unless the statement of the exercise stipulates otherwise.

Answer 1

\[y^2dx-x(2x+3y)dy=0\]

Answer 2

@jiteshmeghwal9

Answer 3

i try to start this but i cant do it lol

Answer 4

It is a homogeneous differential equation \[\frac{dy}{dx}=\frac{y^2}{2x^2+3xy}......(1)\]substitute y=vx then\[\frac{dy}{dx}=v+x \frac{dv}{dx}.......(2)\]substitute (2) in (1).

Answer 5

\[v+x \frac{dv}{dx}=\frac{v^2}{2+3v}\]\[x \frac{dv}{dx}=\frac{-4v^2-2v}{2+3v}\]\[\frac{(2+3v)}{-4v^2-2v}dv=\frac{dx}{x}\]integrate both sides

Answer 6

can u solve it further ?

Answer 7

how can i determine the problem if homogeneous or linear?

Answer 8

If the function satisfies the condition \[f(\lambda x, \lambda y)=\lambda ^n f(x,y) \] then the the function is homogeneous

Answer 9

lol i didnt see, its already the miscellaneous exercises i was solving lol

Answer 10

LOL

Answer 11

its the mixture of several topic problems, but im checking for linear

Answer 12

well this one is homogeneous

Answer 13

(3xy-4y-1)dx +x(x-2)dy=0 <--- this one is linear right?

Answer 14

@jiteshmeghwal9

Answer 15

yes

Answer 16

ill open another post for your medal ^.^ we work for this..

Answer 17

LOL