Question
Asked Jun 10, 2019
36 views

Solve the given initial value problem by using the method of exactness. 

xy dx+(2x2+3y2-20)dy=0, y(0)=1

check_circle

Expert Answer

Step 1

First identify M and N and check that the differential equation is exact.

help_outline

Image Transcriptionclose

хуdx + (2x? + Зу? — 20)dy 0 Consider the differential equation M (x, y) N(x, y)dy 0 Let, M %3D ху, N 3D 2x2 + 3у2 — 20 дм ӘN х, дх 4x ду The given equation is not exact because My(x, y) Nr(x, y)

fullscreen
Step 2

Hence, the given equation is not exact, then we can find the integrating factor and multiply the integrating factor and make it exact differential equation.

help_outline

Image Transcriptionclose

[N,(х, y) — м, (х, у)] -к0) M(х.у) 1 [4х — х] xy 1 k(у) у It follows that eK(V)dy=e'5dy = eln (y) = y, is an integrating factor. Multiplying the given differential equation by produces the exact differential equation. (2x2 + Зу? — 20) dy 0 хаx + y

fullscreen
Step 3

By multiplying the integrating factor, the solution become exact,...

help_outline

Image Transcriptionclose

(2x2+3у?-20) М — х, N У

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Advanced Math

Related Advanced Math Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: Pls explain to me step by step and dont skip any steps. pls write clearly.  i will rate your answer ...

A: To compute the matrix e^tA and use it to solve the given matrix initial value problem

question_answer

Q: Evaluate the Laplacian of the function zx2 x2 + y2+ z2 p(x, y,z)- (a) directly in Cartesian coordina...

A: (a) Let us calculate the Laplacian of the function directly in Cartesian co-ordinates :

question_answer

Q: Find the first five nonzero terms in the solution to the initial value problem: (2+x2)y"-xy'+4y=0, y...

A: Consider the differential equation

question_answer

Q: For this question you need to use Combination, Permutation and Complement principal.

A: As per norms, the first three  questions are answered. To find the number of element in various comb...

question_answer

Q: For an initial investment of 100, an investment yields returns of Xi  at the end of period i for i=1...

A: Given that, the initial investment is 100 and the investment yield is X1 and X2 at the end of period...

question_answer

Q: Vector spaces 2 Pratice not test all of it

A: 35AObtain the standard matrix of the transformation as follows.Given that standard basis for P2 is {...

question_answer

Q: pls explain to me step by step. pls dont skip any steps. thanks

A: Proof:The metric defined on R is d (x, y) = |x – y|.In order to prove the real line is a metric spac...

question_answer

Q: Find the general solution to the given differential equation. 4y"+8y'+8y=0

A: Find the solution of the differential equation.

question_answer

Q: See attachment for question.

A: Click to see the answer