Answered

Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Solve IVP 2y"'-6y" +7y' 3y = 0, y(0) = 1, y'(0) = 0, y" (0) = -5

Sagot :

thakurayushanand3

Answer:

Step-by-step explanation:

This is a second degree, homogeneous differential Equation.

Here’s how this works:

Set y = e^(rx) .

Then, y’ = r*e^(rx) and y’’ = r^2*(e^(rx)).

When I plug everything in, I get the following characteristic equation:

r^2 +3*r +7 = 0

Solving for r, I get

r1 = (-3 +i*sqrt(19))/2 and r2 = (-3-i*sqrt(19))/2

So, your solution will look like the following:

y = e^(-3/2*x) [A*cos(x*sqrt(19)/2) + B*sin(x*sqrt(19)/2)]

Now, you want to use the initial conditions to solve for A and B.

y(0) = 1 means when x =0, y = 1.

We know that A = 1.

y’(0) = 2 means when x = 0, y’ = 2.

To solve for B, you can take the derivative. It involves the product Rule. Replace x with 0 and y’ with 2. You’ll be able to find B. I hope this helps.

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.