this is what i have:for n=0, \int_{0}^{1}\left(1-x\right)^{0}*e^{x}\, dx = e-1
for n=1, \int_{0}^{1}\left(1-x\right)^{1}*e^{x}\, dx = e-2
for n=2, \int_{0}^{1}\left(1-x\right)^{2}*e^{x}\, dx = 2e-5
for n=3, \int_{0}^{1}\left(1-x\right)^{3}*e^{x}\, dx = 6e-16
for n=4...
Re: Differential equation problem
Sorry. I should have posted the original DE before
$$P'_{02}(t)+(\lambda_3+\mu_3)P_{02}(t)=P_{01}(t) \lambda_2$$
and then I used integrating factor $$e^{\int_0^t (\lambda_3+\mu_3) dt}$$ and arrive at the equation
$$\dfrac{d}{dt} [P_{02}(t) \cdot...
Hello,
I am solving an equation using integrating factor. I have come up to a specific point which is $$\dfrac{d}{dt} P_{02}(t) \cdot e^{(\lambda_3+\mu_3)t}=\lambda_2 \cdot P_{01}(t) \cdot e^{(\lambda_3+\mu_3)t}$$
from the previous equation, I have found $$P_{01}(t)=\lambda_1 \int_0^t...