# First and Second Order Differential Equation

1. Homework Statement

a) Show that phi(t) = e^2t is a solution of y' - 2y = 0 and that C*phi(t) is also a solution for any constant C

b) Show that phi(t) = 1/t is a solution of y' + y^2 = 0 for t>0 but that y = c*phi(t) is not a solution unless c = 0 or c = 1

2. Homework Equations

What do they mean by "show'?

3. The Attempt at a Solution

a) dy/2y = dt

(1/2)ln(y) = t + C

y = e^(2t + c) = Ce^2t, where c is any constant

Now what?

b) -dy/y^2 = dt

1/y = t + C

y = 1/(t + C)

Again, how do i show?

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tiny-tim
Homework Helper
Hi aznkid310! a) dy/2y = dt

(1/2)ln(y) = t + C

y = e^(2t + c) = Ce^2t, where c is any constant

Now what?
That's it! You've done it! b) -dy/y^2 = dt

1/y = t + C

y = 1/(t + C)

Again, how do i show?
Again, that's it … except of course you still have to make the obvious remark that C/t is not a solution! What do they mean by "show'?
I think they just mean "prove". Alternatively, they may mean "no need to pretend you don't know the answer … just plug the answer straight in to the original equation and confirm that it works" Better ask your teacher/tutor/professor which one it is! Dick