Question

dy/dx=(x*y)/(y²+x²)

Answer 1

do you want to find the function?? is it a differential equation??

Answer 2

sorry the question was interrupted.
the question is:
- is it homogenous
- solve the deq

Answer 3

1.for any equation to be homogeneous, the total power in denominator and numerator must be same and hence they are variable separable. in your case, numerator power = 2 and denominator power = 2.
2. in order to find the degree of equation, find the power of the highest derivative, which in your case is dy/dx and so its power is 1 and hence its degree is 1.

Answer 4

sorry i read 2nd part as degree...
for second part simply use the variable separatio techniques. y = tx

Answer 5

so just like (y²+x²)dy=x*y dx ?

Answer 6

No... first use substituion. first devide the whole equation by x in numerator and denominator and find a way to get it in f(y/x) form. Is easy

Answer 7

then you put y = tx . so dy/dx = t + x * dt/dx
substitute this in equation for dy/dx and so the whole right side is also in f(t). Know proceed ahead with this.

Answer 8

Sorry i recently got a warning that i am telling answers, so can say any answers now. I didn't now that before. I hope this much hint is good enough

Answer 9

sorry in hurry i did a silly mistake, devide that equation by x^2, as you need to get every thing as a function of y/x.