I need some help here because I am completely lost!!!
I need to solve the ODE (1-x)y''-y'+xy=0 using the initial conditions of y(0)=1, y'(0)=1.
So far I have (1-x)y''-y'=-xy and (1-x)y''=-xy+y' but this is where I got lost. I know it's something really simple but I still can't seem to find the error and I don't know where to go next!!!
I have to find the general pattern and show my final answer is equal to y=e^x...
Thanks for the help!!!!!!!