I have the following initial value problem $$k(x):=0.00025+10^{(6.3+0.027 \cdot x-10)}$$ $$s(x):= 0.0006+10^{(4.716009+0.06\cdot x-10)}$$ $$ \frac{dy}{dx} = (\log(1+0.05)+s(x)+k(x))y(x)+1, y(68)=0$$ I solved this differential equation and found y(t). I evaluated in 0, ie y(0) and found a number around 10 . I would like to confirm this by using eulers method, but i have 2 problem . 1. I'm not sure it is possible to have a starting value greater than the one i would find, 2. if I implement a one that can, I don't get the value i hoped.
My question, is it possible to use this do this? Maybe do a few iteration for me ? If i choose step size 0.5 im getting $$y(67.5) = 0+(-0.5) * (\log(1.05)+s(68)+k(68))y(68)+1)=-0.5$$ is this correct?