Need help with this wronskian problem y1(x)=e^(x) * cosx & y2(x)=e^(x) * sinx Find the values...

Question

Question

Need help with this wronskian problem

y1(x)=e^(x) * cosx & y2(x)=e^(x) * sinx

Find the values of the wronskian y1,y2

Determine if the solutions are linearly independent

Answer 1

✔ Recommended Answer

Answer #1

7:37 5 TOD en con 7,- + : | Kindly rate the solution on merit. In case of further explanation for any step, please leave a co

Answer 2

Similar Homework Help Questions

3 Question 25 Given a set of DE solutions: y1(x) = e* cos x and y2(x)...

3 Question 25 Given a set of DE solutions: y1(x) = e* cos x and y2(x) = e sinx, a) Find the value of the Wronskian W[ v1.y2). b) Determine if the solutions Y1, Y2 are linearly independent. a)W=e b) Linearly Independent a) W=-ex b) Linearly Independent O a) W = 1 b) Linearly Independent a) W=eX b) Linearly Dependent O a) W=0 b) Linearly Dependent None of them
4. Find the Wronskian for y1 = x , y2 = cos(2x), and y3 = e...

4. Find the Wronskian for y1 = x , y2 = cos(2x), and y3 = e . 4. (10 points) Find the Wronskian for yı = 23, y2 = cos(2x), and y3 = e3r.
Please prove this solution and explain why y2 can be taken as (x^2)(y1) Problem 2. Find the general solution of the equation Note that one of two linearly independent solutions is yi(r) -e. Solution....

Please prove this solution and explain why y2 can be taken as (x^2)(y1) Problem 2. Find the general solution of the equation Note that one of two linearly independent solutions is yi(r) -e. Solution. Using Abel's formula, we get the following relations for the Wronskian dW pi dW 2r1 On the other hand, Comparing these two expression for W(x), we can take y2 :- r2yı. Correspondingly, the general solution is Problem 2. Find the general solution of the equation Note...

Problem #1 Y1(x)= x and Y2(x)=e* are linearly independent solution of the homogeneous equation: (x-1)y"-xy'+y =...

Problem #1 Y1(x)= x and Y2(x)=e* are linearly independent solution of the homogeneous equation: (x-1)y"-xy'+y = 0 Find a particular solution of (x-1) y”-xy’+y = (x-1)} e2x
Ch3.2- Existence Uniqueness Wronskian: Problem 3 Previous Problem Problem List Next Problem (1 point) Use the...

Ch3.2- Existence Uniqueness Wronskian: Problem 3 Previous Problem Problem List Next Problem (1 point) Use the Wronskian to determine whether the functions yı = sin(62) and y2 = cos(4.c) are linearly independent. Wronskian = det These functions are linearly independent because the Wronskian is nonzero for Choose value(s) of 2.
Two linearly independent solutions of the differential y" - 4y' + 5y = 0 equation are...

Two linearly independent solutions of the differential y" - 4y' + 5y = 0 equation are Select the correct answer. 7 Oa yı = e-*cos(2x), Y1 = e-*sin(2x) Ob. Y1 = et, y2 = ex Oc. yı = e cos(2x), y2 = e* sin(2x) Od. yı=e2*cosx, y2 = e2*sinx Oe. y = e-*, y2 = e-S*

find the series using the maclaurin series for e^x, sinx, and cosx e - cos(x) -isin(ix) e - cos(x) -isin(ix)

find the series using the maclaurin series for e^x, sinx, and cosx e - cos(x) -isin(ix) e - cos(x) -isin(ix)
17. Another way to check if y1, y2 are linearly INDEPENDENT in an interval I is:...

17. Another way to check if y1, y2 are linearly INDEPENDENT in an interval I is: for all I for all I does not exist for all I d. none of the above 18. If y1 is a solution of the equation y "+ P (x) y '+ Q (x) y = 0, a second solution would be y2 (x) = u (x) y1 (x) where u (x) it is: d. all of the above 19. The following set...
lPLS SHOW ALL WORK Problem 6. Prove that the family of functions {Y1 = 1, y2...

lPLS SHOW ALL WORK Problem 6. Prove that the family of functions {Y1 = 1, y2 = e", y3 = 222} is linearly independent on (-00,00). Find a homogeneous linear equation whose general solution is y = C1 + C2e? + C2e2^ .

find Y1=, Y2=, and W(t)= (1 point) Find the function yi of t which is the...

find Y1=, Y2=, and W(t)= (1 point) Find the function yi of t which is the solution of 25y" – 40y' + 12y = 0 y(0) = 1, yf(0) = 0. with initial conditions Yi = Find the function y2 of t which is the solution of 25y" – 40y' + 12y = 0 with initial conditions Y2 = Find the Wronskian W(t) = W(y1, y2). W(t) = Remark: You can find W by direct computation and use Abel's theorem...