Form of Solution for First Order ODE T'(t) - (1 - n^2/4)T(t) = 0

[leopard]

y'(t) - ay(t) = 0

What is the form of the solution? $$C \cdot e^{at}$$

?I have this ODE:

$$T'(t) - (1 - \frac{n^2}{4})T(t) = 0$$

If I'm right, the solutions should be of the form

$$C \cdot e^{(1- \frac{n^2}{4})t}$$

My book, however, says $$C \cdot e^ {1- \frac{n^2}{4}t}$$

Who's right?

 

[Office_Shredder]

I think the book forgot some parentheses

 

[leopard]

Brilliant.

And how about the equation

y' = (y - x)^2

what's the form of the solution here?

I find it hard to determine the form of solution of differential equations.

 

[Dick]

I would try a simple substitution first. How about v=y-x? Now see if you can separate it in those variables.