Consider the initial value problem: y0 = 3 + x−y, y(0) = 1 (a)
Solve it analytically. (b) Solve it using Euler’s method using step
size h = 0.1 and find an approximation to true solution at x = 0.3.
(c) What is the error in the Euler’s method at x = 0.3
Consider the following differential equation:
x2y"-2xy'+(x2+2)y=0
Given that y1=x cos x is a solution, find a second
linearly independent solution to the differential equation.
Write the general solution.
Given:
f(x,y) = 5 - 3x - y for 0 < x,y < 1 and x + y < 1, 0
otherwise
1) find the covariance of x and y
2) find the marginal probability density function for x
c) find the probability that x >= 0.6 given that y <=
0.2