Hi, I submitted this question on here the other day a user suggested some topics which might help so I have went away and tried this and this is what I have came up with. I just want to know what I have so far is right also I need help with integrating the rhs of the equation.
The question is
dy/dx + 0.8y = 0.6 e-1.4x y(0)=1
I have to solve the ODE to the given condition using exact methods and evaluate the solution y for x = 0.0 to x=0.5 in steps of 0.05.
dy/dx + P(x)y = Q(x)
The Attempt at a Solution
so I my working so far is
dy/dx + 0.8y = 0.6 e^-1.4x
P(x) = 0.8
IF = e ^ ∫P(x) dx
IF = e ^∫0.8 dx
= e ^ 0.8x
e0.8x* dy/dx + e0.8xy = e0.8x*0.6e-1.4x
Therefore e0.8x = ∫ e0.8x*0.6e-1.4x
This is where I get stuck. What I have done so far is this correct and what should I do to progress from this point? I don't understand how to do the integration on the rhs.