First order linear differential equations help?

Question

I just have a single question about this differential equation. Use first order of linear differential equation to solve this problem:

2(dy/dx) = 5 - 6y

I know the equation is (dy/dx) + P(x) y = Q(x) so my question is what do I do with the 2 that's in 2(dy/dx)? So far I did 2(dy/dx) + 6y = 5

ted s · Accepted Answer

dy / dx + 3 y  = 5 / 2 ---> y = c1 e^(-3x) +  5 / 6

shafeer · Answer

2(dy/dx)=5-6y
2dy/5-6y=dx
which is in variable separable form
integrating both sides
2logl5-6yl/-6=x+c



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MechEng2030 · Answer

2(dy/dx) = 5 - 6y

This is actually seperable:

dy/(5 - 6y) = dx/x

Integrating both sides:

-1/6*ln|5 - 6y| = ln|x| + C

solve for y.

First order linear differential equations help?

3 Answers