Prove that equation is in the form dy/dx = G (ax + by) and solve:

Question

thank u!

Answer 1

z = x + y; dy/dx = dz/dx - 1;

dz/dx - 1 = √z - 1; dz/dx = √z; ∫z^-1/2dz = ∫dx; 2√z = x + C; 2√x + y = x + C; y = (x + C)²/4 - x

Answer 2

If you set up the following, "the pieces of the puzzle should fall into place"

The simplest iteration of the seemingly infinite answers would make:

a = 1

b = 1

So now the problem reduces to:

dy/dx = G( x + y )

Now, I propose we state that:

t( x, y ) = x + y

So, therefore:

dy/dx = √( t ) - 1

dy/dx = G(t)

Now, since both equations are stating that they are equal to dy/dx, then, it can be reasoned that:

G(t) = √( t ) - 1

I hope this helps! Message me in the comments with any questions, comments, or concerns!