Solve Differential Equation dy/dx = x + y for General Solution

[quantum13]

I read this in my calculus first year textbook, and I am just curious.

Homework Statement

For differential equation dy/dx = x + y, the general solution is y = Ce^x - x -1 (the solution of which is beyond this course). Verify this by solving dy/dx.

Homework Equations

calculus equations

The Attempt at a Solution

dy/dx = Ce^x - 1

this looks nothing like x + y however. what am I missing?

 

[mbisCool]

x + y = x + Ce^x-x-1=Ce^x-1

Simply substitute your solution into the original differential equation to verify.

 

[quantum13]

Thanks! At least it's a trivial solution, which kind of makes me feel better, but not really =]

 

[njama]

I will do the same on this way:

y' = x+y

y=Ce^x - x -1

y'=Ce^x-1

Ce^x-1=y+x

y=Ce^x-1-x