How Do You Solve These Differential Equations Using Separation of Variables?

[fran1942]

Hello, I have just started learning differential equations.
I am stuck on solving these two by separating the variables and writing the general solution.
Can someone please show me the procedure.

1. dy/dx = 1/y

2. xdy/dx = y

Thanks kindly for any help.

 

[Simon Bridge]

Think the dy and dx as functions of x and y respectively, so dy/dx is just an ordinary division. Separation of variables is just the same as algebra - you need to get all the terms with a y on one side of the equals sign and all the terms with an x on the other side.

so for:
dy/dx=x you multiply both sides by dx to get dy=x.dx

then you just write an integration sign in front of each expression.
∫dy = ∫x.dx

now you follow that procedure for your examples.