Solve the homogeneous equation dy/dx = x^2 + y^2 / xy?

Answer 1

dy/dx = x^2 + y^2 / xy
rearrange the equation:
dy/dx-y/x=x^2
here we use the integrating
factor method which applies
to equations of the form,
dy/dx+g(x)y=h(x)
1)determine the integrating factor
p=e^(int(-1/x)dx)
=e^(-lnx)=e^(ln(1/x))=1/x
2)the equation can now
be written
d/dx(y/x)=1/x*(x^2)= x
3)integrate this last equation
to obtain
y/x=int(x)dx=x^2/2+C
4)the general solution is
therefore,
y= x^3/2+Cx
where C is an arbitrary constant

{check answer
dy/dx= 3x^2/2+C
y/x= x^2/2 +C
dy/dx-y/x
=3x^2/2+C-x^2/2-C
= 2x^2/2= x^2
{the rearranged equation}

i hope that this helps

Answer 2

Sorry i have 2 agree wth trickyric if u cant work out the answer u dont need 2 know or all ready know did u read it some ware perhaps

Answer 3

dy/dx = x^2 + y / x
dy = x^2dx + (y / x) dx

y=1/3 * x^3 + y* ln|x| + C

Answer 4

let y = vx
dy/dx = v + x dv/dx

v + x dv/dx = x² + v²x² / vx²
v + x dv/dx = x² + v

x dv/dx = x²
dv/dx = x

∫dv = ∫x dx
v = x²/2+ C
y/x = x²/2 + C
y = x³/2 + Cx

Answer 5

First you have to know what you're solving for.

Answer 6

No.