# Thread: Can you solve this equation?

2. ## Re: Can you solve this equation?

Have you tried putting the ODE into standard linear form and computing the integrating factor?

3. ## Re: Can you solve this equation?

i would definitely try that if i knew how to do it. however.

4. ## Re: Can you solve this equation?

Hi rjohn39 !
Did you ever solve this equation : (A*x+B)*y'(x) + y(x) = 1 ?
It is exactly le same equation that your equation (only the notations are changed)

5. ## Re: Can you solve this equation?

Hi JJ. No, actually, I have never solved the equation you refer to. It would definitely help if I had!

7. ## Re: Can you solve this equation?

Originally Posted by rjohn39
Hi JJ. No, actually, I have never solved the equation you refer to. It would definitely help if I had!
It is one of the most simple linear ordinary differential equation of the first order. I am sure that the method to solve it is explained in your textbook.
The first step consists in solving the homogeneous equation (A*x+B)*y'(x) + y(x) =0 (separate the variables)
The second step is to find a particular solution of the whole equation (A*x+B)*y'(x) + y(x) =1 (obvious)
The third step is to add the results of the two preceeding steps in order to obtain the general solution.
Sorry, it is not of use to detail on the forum what one can find in any texbook on differential equations.
Good work !