Check general solution to ODE please

[Lengalicious]

Ok I'm new to ODE's so yeh, just to double check here's what I've 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

 

[HallsofIvy]

Why not check it yourself- differentiate that function!

 

[xplosiv3s]

Ok I'm new to ODE's so yeh, just to double check here's what I've 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

don't forget +C

 

[Lengalicious]

don't forget +C

Ah of course, thanks =)

 

[Lengalicious]

Why not check it yourself- differentiate that function!

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

 

[xplosiv3s]

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

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)