Solving a Differential Equation with Special Integrating Factor

[kuahji]

dy/dx=2+\sqrt{y-2x+3}

The only way we've been taught to solve differential equations so far is, separation of variables method, exact equation, bernoulli equation, homogeneous, and we're about to start special integrating factor.

I can't seem to get the equation into any of the first forms listed. Which leads me to believe its a special integrating factor problem. Or am I incorrect in this assumption?

 

[rootX]

dy/dx=2+\sqrt{y-2x+3}

The only way we've been taught to solve differential equations so far is, separation of variables method, exact equation, bernoulli equation, homogeneous, and we're about to start special integrating factor.

I can't seem to get the equation into any of the first forms listed. Which leads me to believe its a special integrating factor problem. Or am I incorrect in this assumption?

I would say try substitution v = y-2x

 

[Dick]

Why don't you try a change of variable v=y-2*x+3 before resorting to extreme measures? It looks dead simple to me.