Question

Under "Basic DE's; Check Yourself; Take the quizzes; Separation of Variables (PDF)," why isn't there a +- in front of Ce^2x?

Answer 1

Here is the original equation: \[dy/dx = 2y +1\] After exponentiation we remove the absolute value bars leaving: \[2y+1 = \pm Ce ^{2x}\] Solving through, we would get: \[y = \pm Ce ^{2x} -1/2\] Not \[y = Ce ^{2x} -1/2\] As stated in the answer key, correct? Or does the constant C "absorb" the \[ \pm \] ?

Answer 2

Never mind; it's as I thought --> C accounts for it.