# Homework Help: Check general solution to ODE please!

1. Mar 1, 2012

### Lengalicious

Ok I'm new to ODE's so yeh, just to double check heres what ive done:

Question: Find the general solution to the following differential equation:
Equation: y'(x) = sec2 (3x + 1)

My answer: Don't I just integrate? So dy/dx = sec2 (3x + 1)

then, y = sec2 (3x + 1) dx

so y = (tan(3x+1))/3

2. Mar 1, 2012

### HallsofIvy

Why not check it yourself- differentiate that function!

3. Mar 1, 2012

### xplosiv3s

don't forget +C

4. Mar 2, 2012

### Lengalicious

Ah of course, thanks =)

5. Mar 2, 2012

### Lengalicious

I wasn't worried as to whether my integration was wrong I was worried as to whether my methodology was wrong or not.

6. Mar 2, 2012

### xplosiv3s

Yes, you are correct but what he said will help verify wether your methodology is correct or not, because an appropriorate one would of course lead to the correct solution :)

as a rule of thumb:

when y=sec2(αx+b) and you want to find the integral:

then ∫sec2(αx+b)dx = 1/α*tan(αx+b)