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Problem #16: [2 marks] A solution, y = f(x), of the differential equation, x²y + 5x²y...
Problem #2: Let y(x) be the solution to the following initial value problem. x4 y' + 5x> y = Inça), x>0, y(1) = 5. Find y(e). Problem #2: O Problem #2: Enter your answer symbolically, as in these examples Just Save Submit Problem #2 for Grading Problem #2 | Attempt #1 | Attempt #2 | Attempt #3 Your Answer: Your Mark:
o2: 16 Marks] Find the general solution of the differential equation (sin x)y" +(cos x)y' cos x by reduction to first order DE.
o2: 16 Marks] Find the general solution of the differential equation (sin x)y" +(cos x)y' cos x by reduction to first order DE.
Consider the following differential equation.
(1 + 5x2) y′′ − 8xy′
− 6y = 0
(a)
If you were to look for a power series solution about
x0 = 0, i.e., of the form
∞
Σ
n=0
cn xn
then the recurrence formula for the coefficients would be given by
ck+2 =
g(k) ck , k
≥ 2. Enter the function g(k) into the answer
box below.
(b)
Find the solution to the above differential equation with
initial conditions y(0) ...
Problem #7: Let f(x) 2 5x, -7<x<7. Find the complex Fourier series forf and then, (a) enter the value of co. (b) enter the value of cn for n0. (Your expression must be fully simplified.) Enter your answer symbolically, as in these examples Problem #7(a) Enter your answer as a symbolic function of i,n, as in these examples Problem #7(b)
Problem #12: Find the particular solution to the differential equation y - VX) = -xe-* with the condition y = 1 when x = 1. Problem #12: Enter your answer as a symbolic function of X, as in these examples Problem #13: Suppose that X is a random variable with an exponential distribution with parameter 1 - 5. Find the probability P(X ) Problem - 13:
y = 3x0+ QUESTION 2 Solve the given differential equation. (The form of yp is given D2y + 25y = -5 sin 5x (Let y p = Ax sin 5x + Bx cos 5x.) sin 5x + c2 cos 5x + x sin 5x - 1 x cos 5x Oo oo cos 5x + = x cos 5x y = C1 sin 5x + C2 cos 5x + 5x sin 5x y = C1 sin 5x + C2 cos 5x...
1. Let y = f(x) be the solution to the differential equation = y - x. The point (5,1) is on the graph of the solution to this differential equation. What is the approximation for f() if Euler's Method is used, starting at x = 5 with a step size of 0.5?
Problem #4: Use separation of variables to find a product solution to the following partial differential equation, Ou (5y + 8) ou си + (3x + 6) oy = 0 that also satisfies the conditions u(0,0) = 9 and ux(0,0) = 8. Problem #4: Enter your answer as a symbolic 9*e^(1/9)*(3*x^2/2+6*X-5*y^2/2-function of x,y, as in these examples + 6x - 9e1/9(3 + 52 - 8y) Just Save Submit Problem #4 for Grading Problem #4 Attempt #1 Attempt #2 Attempt #3...
Let y(x) be the solution to the following initial value problem. dy dx In x = -2 xy y(1) = 4 Find y(e). Enter your answer symbolically, as in these examples
Determine if the given function y- f(x) is a solution of the accompanying differential equation Differential equation: 9xy' + 9y-cos x Initial condition: y()0 Solution candidate: y- x O a. No b. Yes
Determine if the given function y- f(x) is a solution of the accompanying differential equation Differential equation: 9xy' + 9y-cos x Initial condition: y()0 Solution candidate: y- x O a. No b. Yes