In Problems 31 and 32 find values of m so that the function y = xm...
Sect. 4.2. Reduction of Order 1. In the following problems, the indicated function y(x) is a solution of the given differential equation. (a). Use the method of reduction of order, i.e., the formula 32(x) = x1(1) one-Plade de to find the second linearly independent solution 72(2). (b). After having determined yz(x), write down the general solution: y(x) = 4(x) + C292(2) The problems are given as follows: (1). 2y" – 7y' + 3y - 0, y = */2 (Answer: 92(x)...
For Problems 22-25, determine all values of the constant
r such that the given function solves the given
differential equation.
For Problems 22–25, determine all values of the constant r such that the given function solves the given differential equation. 24. y(x) = x", x2y" + xy' – y = 0.
#32
U. + 2y + y + 1 -e: y(0) = 0, y'(o) - 2 In Problems 31-36, determine the form of a particular solution for the differential equation. Do not solve. 31. y" + y = sin : + i cos + + 10' 32. y" - y = 2+ + te? + 1221 x" - x' - 2x = e' cos - + cost y" + 5y' + 6y = sin t - cos 2t 35. y" –...
Given two functions, M(x, y) and N(x,y), suppose that ON/ that an/az-amay is M-N a function of x +y. That is, let f(t) be a function such that ON _ OM dc du f(x+y) = M-N Assume that you can solve the differential equation Mdx + Ndy = 0 by multiplying by an integrating factor u that makes it exact and that it can also be written as a function of x + y, u = g(x + y) for...
The function Y(t) = t is a solution of the differential equation (t2+4)y" - 2ty' + 2y = 0. Find a real general solution of this equation.
1. The function: y, = e' is a solution of the homogeneous linear equation: y"-2y'+ y = 0. Use Reduction of Order to find a second linearly independent solution, then write the general solution for the differential equation: y" - 2y'+y=0
In Problems 7 and 8 find the general solution of the given differential equation. 8. y′′ + 2y′ + 5y = g(t), (a) g(t) = −2t + 4t2; (b) g(t) = t3;
In Problems 1 through 10, find a function y = f(x) satisfy. ing the given differential equation and the prescribed initial condition. 1.dy = 2x + 1;y(0) = 3
In Problems 1 through 10, find a function y = f(x) satisfy. ing the given differential equation and the prescribed initial condition. 1.dy = 2x + 1;y(0) = 3
7. Find cov(X, Y)
8. Are the random variables X, Y independent? Justify
answer
Edit : do not solve number 1, I already solved.
C=3/32
Use this information for problems 1 -8: Let X, Y be two continuous random variables and let f(x, y)2y + xy?) over the range O< x<2 and 0< y< 2. Determine the v function alue of the constant c that makes this function a joint probability density 1.
Use this information for problems 1 -8:...
4. The function y(x) = r2 is a solution of the given differential equation. Use an appropriate formula to find a second solution y(x). xy" + 2xy' - 6y = 0.