Answer:
[tex]ydv = (v +2)dy\\[/tex]
Step-by-step explanation:
We are given the following differential equation:
[tex]y dx = 2(x + y) dy[/tex]
We have to substitute
[tex]x = vy[/tex]
Differentiating we get,
[tex]\dfrac{dx}{dy} = v + y\dfrac{dv}{dy}[/tex]
Putting value in differential equation, we get,
[tex]y dx = 2(x + y) dy\\\\y\dfrac{dx}{dy}=2(x+y)\\\\y(v+y\dfrac{dv}{dy}) = 2(vy + y)\\\\vy + y^2\dfrac{dv}{dy} = 2vy +2y\\\\y^2\dfrac{dv}{dy}=vy +2y\\\\y^2dv = y(v+2)dy\\ydv = (v +2)dy\\[/tex]
is the differential equation after substitution.
