Homework Answers
Add Answer to:
2. Consider the homogeneous equation r2y"- (3r2 2x)y (3x + 2)y= 0. (a) Verify that y...
2) (25 points) a) (5 points) Verify that y= eat is a solution of the homogeneous...
2) (25 points) a) (5 points) Verify that y= eat is a solution of the homogeneous differential equation y" - 12y' + 36 y = 0. b) (15 points) Use the method of reduction of order to find a second solution 72 of the given homogeneous equation and a particular solution y of the nonhomogeneous differential equation y" - 12y' + 36 y = 36. e) (5 points) Can you write the general solution of the nonhomogeneous differential equation y"...
1. Consider the equation xy" - 2y' + (2 - x)y = 0,x > 0. We...
1. Consider the equation xy" - 2y' + (2 - x)y = 0,x > 0. We can easily verify that y(x) = e* is a solution of the equation. Use reduction of order to determine the general solution of the equation.
Consider the differential equation 4x2y′′ − 8x2y′ + (4x2 + 1)y = 0 (a) Verify that x0 = 0 is a regular singular point of...
Consider the differential equation 4x2y′′ − 8x2y′ + (4x2 + 1)y = 0 (a) Verify that x0 = 0 is a regular singular point of the differential equation and then find one solution as a Frobenius series centered at x0 = 0. The indicial equation has a single root with multiplicity two. Therefore the differential equation has only one Frobenius series solution. Write your solution in terms of familiar elementary functions. (b) Use Reduction of Order to find a second...
Consider the homogeneous linear third order equation A) xy'''−xy'' + y'−y = 0 Given...
Consider the homogeneous linear third order equation A) xy'''−xy'' + y'−y = 0 Given that y1(x) = e^x is a solution. Use the substitution y = u*y1 to reduce this third order equation to a homogeneous linear second order equation in the variable w = u'. You do not need to solve this second order equation. B.) xy''' + (1−x)y'' + xy'−y = 0. Given that y1(x) = x is a solution. Use the substitution y =...
(1 point) We consider the non-homogeneous problem y" +2y +2y 20os(2x) First we consider the homogeneous...
(1 point) We consider the non-homogeneous problem y" +2y +2y 20os(2x) First we consider the homogeneous problem y" + 2y' +2y 0 1) the auxiliary equation is ar2 br 2-2r+2 2) The roots of the auxiliary equation are i 3) A fundamental set of solutions is eAxcosx,e xsinx (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary solution yc-c1Y1 + c2y2 for arbitrary constants c1 and c2. Next...
3. Consider the differential equation ty" - (t+1)y + y = t?e?', t>0. (a) Find a...
3. Consider the differential equation ty" - (t+1)y + y = t?e?', t>0. (a) Find a value ofr for which y = et is a solution to the corresponding homogeneous differential equation. (b) Use Reduction of Order to find a second, linearly independent, solution to the correspond- ing homogeneous differential equation. (c) Use Variation of Parameters to find a particular solution to the nonhomogeneous differ- ential equation and then give the general solution to the differential equation.
We consider the non-homogeneous problem y" + 2y + 2y = 40 sin(2x) First we consider...
We consider the non-homogeneous problem y" + 2y + 2y = 40 sin(2x) First we consider the homogeneous problem y" + 2y + 2y = 0: 1) the auxiliary equation is ar? + br +C = 242r42 = 0. 2) The roots of the auxiliary equation are 141-14 Center answers as a comma separated list). 3) A fundamental set of solutions is -1 .-1xco) Center answers as a comma separated list. Using these we obtain the the complementary solution y...
1. The function: y, = e' is a solution of the homogeneous linear equation: y"-2y'+ y...
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
Given yı(x) = x4 satisfies the corresponding homogeneous equation of x+y" + 3xy' – 24y =...
Given yı(x) = x4 satisfies the corresponding homogeneous equation of x+y" + 3xy' – 24y = 21x + 48, x > 0 Then the general solution to the non-homogeneous equation can be written in the form y(x) = Ax4 + Bx" + Yp. Use reduction of order to find the general solution in this form (your answer will involve A, B, and x) y(x) = Preview
5) Consider the second order linear non-homogeneous differential equation tay" - 2y = 3t2 - 1,t>...
5) Consider the second order linear non-homogeneous differential equation tay" - 2y = 3t2 - 1,t> 0. a) Verify that y(t) = t- and y(t) = t-1 satisfy the associated homogeneous equation tay" - 2y = 0. (5 points) b) Find a particular solution to the non-homogeneous differential equation. (10 points) c) Find the general solution to the non-homogeneous differential equation. (5 points)
2) (25 points) a) (5 points) Verify that y= eat is a solution of the homogeneous differential equation y" - 12y' + 36 y = 0. b) (15 points) Use the method of reduction of order to find a second solution 72 of the given homogeneous equation and a particular solution y of the nonhomogeneous differential equation y" - 12y' + 36 y = 36. e) (5 points) Can you write the general solution of the nonhomogeneous differential equation y"...
1. Consider the equation xy" - 2y' + (2 - x)y = 0,x > 0. We can easily verify that y(x) = e* is a solution of the equation. Use reduction of order to determine the general solution of the equation.
(1 point) We consider the non-homogeneous problem y" +2y +2y 20os(2x) First we consider the homogeneous problem y" + 2y' +2y 0 1) the auxiliary equation is ar2 br 2-2r+2 2) The roots of the auxiliary equation are i 3) A fundamental set of solutions is eAxcosx,e xsinx (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary solution yc-c1Y1 + c2y2 for arbitrary constants c1 and c2. Next...
3. Consider the differential equation ty" - (t+1)y + y = t?e?', t>0. (a) Find a value ofr for which y = et is a solution to the corresponding homogeneous differential equation. (b) Use Reduction of Order to find a second, linearly independent, solution to the correspond- ing homogeneous differential equation. (c) Use Variation of Parameters to find a particular solution to the nonhomogeneous differ- ential equation and then give the general solution to the differential equation.
We consider the non-homogeneous problem y" + 2y + 2y = 40 sin(2x) First we consider the homogeneous problem y" + 2y + 2y = 0: 1) the auxiliary equation is ar? + br +C = 242r42 = 0. 2) The roots of the auxiliary equation are 141-14 Center answers as a comma separated list). 3) A fundamental set of solutions is -1 .-1xco) Center answers as a comma separated list. Using these we obtain the the complementary solution y...
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
Given yı(x) = x4 satisfies the corresponding homogeneous equation of x+y" + 3xy' – 24y = 21x + 48, x > 0 Then the general solution to the non-homogeneous equation can be written in the form y(x) = Ax4 + Bx" + Yp. Use reduction of order to find the general solution in this form (your answer will involve A, B, and x) y(x) = Preview
5) Consider the second order linear non-homogeneous differential equation tay" - 2y = 3t2 - 1,t> 0. a) Verify that y(t) = t- and y(t) = t-1 satisfy the associated homogeneous equation tay" - 2y = 0. (5 points) b) Find a particular solution to the non-homogeneous differential equation. (10 points) c) Find the general solution to the non-homogeneous differential equation. (5 points)
Most questions answered within 3 hours.
-
16) Which of the following is not a way to reduce the
government's budget
deficit
A)...
asked 1 minute from now -
At some time, a charged particle with q = −1.24×10−8C is moving
with instantaneous velocity v...
asked 7 minutes ago -
4. Determine the theoretical yield of P2O5, when 3.07 g of P
reacts with 6.09 g...
asked 2 hours ago -
Explain the PEST analysis and how a marketer would use this when
putting together a marketing...
asked 1 hour ago -
S sells property with a $500 basis to B for $450, and B later
sells the...
asked 2 hours ago -
True/False Questions
1.
In interpreting an agreement, courts generally apply a
subjective standard.
2.
If, after...
asked 1 hour ago -
On January 1, 20X7, Green Corp. paid $1,020,000 to acquire Wax
Co. Wax maintained separate incorporation....
asked 2 hours ago -
C++
Write a class Fraction that defines adding, subtracting,
multiplying, and dividing fractions by overloading standard...
asked 4 hours ago -
This java code won't run and I can't figure out the problem with
it. Please help...
asked 5 hours ago -
Trace the following recursive methods:
a) isPal with the string “abccda”
b) isAnBn with the string...
asked 6 hours ago -
1. Which of the following is false about photosynthesis?
A. ATP is the molecule used to...
asked 7 hours ago -
A simple random sample of size n=64 is obtained from a
population with a mean of...
asked 8 hours ago