Find the particular solution to the differential equation yV1-x' y' - xv1 -,
condition y(0) = 1.
To find the particular solution to the differential equation, we first need to solve the differential equation:
V1 - x' * y' - xV1 = 0
Rearranging the terms, we get:
V1 = x' * y' + xV1
Now, let's find the solution to this differential equation. First, separate the variables:
dy/dx = (V1 - x * V1) / x = V1 * (1 - x)
Now, we can solve this separable differential equation by integrating both sides:
∫(1/y)dy = ∫(1 - x)dx
ln|y| = x - (x^2)/2 + C
To find C, we use the initial condition y(0) = 1:
ln(1) = 0 - (0)/2 + C
C = 0
So, the particular solution to the differential equation is:
y = e^(x - (x^2)/2)