Question

consider ivp given by x^2y" + 2xy' - 6y = 0 w/ y(1) = 1, y'(1)...

consider ivp given by x^2y" + 2xy' - 6y = 0 w/ y(1) = 1, y'(1) = 2

verify y(x) = x^2 and y(x) = x^-3 are solutions
use wronskian to show both y(x) above are linearly independent
find unique solution to ivp

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the following Initial Value Problem (IVP) y' = 2xy, y(0) = 1. Does the IVP...
Consider the following Initial Value Problem (IVP) y' = 2xy, y(0) = 1. Does the IVP exists unique solution? Why? If it does, find the solution by Picard iteration with y0(x) = 1.
Consider the second-order homogeneous linear equation y''−6y'+9y=0. (a) Use the substitution y=e^(rt) to attempt to find...
Consider the second-order homogeneous linear equation y''−6y'+9y=0. (a) Use the substitution y=e^(rt) to attempt to find two linearly independent solutions to the given equation. (b) Explain why your work in (a) only results in one linearly independent solution, y1(t). (c) Verify by direct substitution that y2=te^(3t) is a solution to y''−6y'+9y=0. Explain why this function is linearly independent from y1 found in (a). (d) State the general solution to the given equation
Solve the initial-value problem. y"-6y'+9y=0; y(0)=2, y'(0)=3 Given that y1=x2 is a solution to y"+(1/x) y'-(4/x2)...
Solve the initial-value problem. y"-6y'+9y=0; y(0)=2, y'(0)=3 Given that y1=x2 is a solution to y"+(1/x) y'-(4/x2) y=0, find a second, linearly independent solution y2. Find the Laplace transform. L{t2 * tet} Thanks for solving!
3. Consider the equation (3x^2y + y^2)dx + (x^3 + 2xy + 5)dy = 0. (a)...
3. Consider the equation (3x^2y + y^2)dx + (x^3 + 2xy + 5)dy = 0. (a) Verify this is an exact equation (b) Solve the equation
7) (1 − x2)y'' − 2xy' + 2y = 0; y(0) = 0, y'(0) = 3...
7) (1 − x2)y'' − 2xy' + 2y = 0; y(0) = 0, y'(0) = 3 Find the power series solution about x=0.
Use a series centered at x0=0 to find the general solution of y"+x^2y'-2y=0. Use a series...
Use a series centered at x0=0 to find the general solution of y"+x^2y'-2y=0. Use a series centered at x0=0 to find the general solution. Write out at least 4 nonzero terms of each series corresponding to the two linearly independent solutions.
find the general solution of the given differential equation 1. y''−2y'+2y=0 2. y''+6y'+13y=0 find the solution...
find the general solution of the given differential equation 1. y''−2y'+2y=0 2. y''+6y'+13y=0 find the solution of the given initial value problem 1. y''+4y=0, y(0) =0, y'(0) =1 2. y''−2y'+5y=0, y(π/2) =0, y'(π/2) =2 use the method of reduction of order to find a second solution of the given differential equation. 1. t^2 y''+3ty'+y=0, t > 0; y1(t) =t^−1
show that y1= e^x and y2=1+x form a basis for the general solution of xy''-(1+x)y'+y=0 by...
show that y1= e^x and y2=1+x form a basis for the general solution of xy''-(1+x)y'+y=0 by verifying that they both work, and are linearly independent using the wronskian.
solve ivp: (y+6x^2)dx + (xlnx-2xy)dy = 0, y(1)=2, x>0
solve ivp: (y+6x^2)dx + (xlnx-2xy)dy = 0, y(1)=2, x>0
find the solution: y'''+2y''-5y'-6y=7t² y(0)=1, y'(0)=3, y''(0)=-1
find the solution: y'''+2y''-5y'-6y=7t² y(0)=1, y'(0)=3, y''(0)=-1
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT