I've been asked to solve the differential equation below with perturbation methods
y''+vy^(1/2)+8=x
where 0<v<<1 (ie. what is usually represented by epsilon)
I know to start by supposing that y=a0 + a1v + a2v^2+...
But I'm lost as to what I should do about the free-standing x, keeping in mind that y is a function of x; I also don't know how exactly the y being to the power of a half will change the perturbation series that I should be trying to replace y with. If someone could clarify these two issues, I should hopefully be able to take the rest on myself.
y''+vy^(1/2)+8=x
where 0<v<<1 (ie. what is usually represented by epsilon)
I know to start by supposing that y=a0 + a1v + a2v^2+...
But I'm lost as to what I should do about the free-standing x, keeping in mind that y is a function of x; I also don't know how exactly the y being to the power of a half will change the perturbation series that I should be trying to replace y with. If someone could clarify these two issues, I should hopefully be able to take the rest on myself.