Question
Asked Jun 8, 2019
1 views

Use the method of integrating factors to solve the initial value problem.

  • y'+xy=x, y(0)=1
check_circle

Expert Answer

Step 1
The first order linear differential equation is y'+xy = x with its initial condition
y(0)=1
The differential equation is of the form yp(x)y=q(x),
where pc) and q(x)
+
are
continuous function and here p(x) = x, q(x)
= X.
Calculate the integrating factor of the above differential equation as follows
|p(x)cd*
IF = J
= e
Thus, the integrating factor is IF = e2.
help_outline

Image Transcriptionclose

The first order linear differential equation is y'+xy = x with its initial condition y(0)=1 The differential equation is of the form yp(x)y=q(x), where pc) and q(x) + are continuous function and here p(x) = x, q(x) = X. Calculate the integrating factor of the above differential equation as follows |p(x)cd* IF = J = e Thus, the integrating factor is IF = e2.

fullscreen
Step 2
Multiply the integrating factor on both sides of the equation y'+ xy =x and simplify.
e2 yxy)
=xe2
x
e2 y'e2 xy = xe2
e
dx
help_outline

Image Transcriptionclose

Multiply the integrating factor on both sides of the equation y'+ xy =x and simplify. e2 yxy) =xe2 x e2 y'e2 xy = xe2 e dx

fullscreen
Step 3
= xe2 with respect to x on both sides
Integrate the simplified equation
e у
dx
d
dx
хе
dx
2
е? у 3е? +С
2 C
2
y e
help_outline

Image Transcriptionclose

= xe2 with respect to x on both sides Integrate the simplified equation e у dx d dx хе dx 2 е? у 3е? +С 2 C 2 y e

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: if three balls are drawn at random, what is the probability that at least one of them is blue?

A: Three balls are randomly drawn from the box.The probability of at least one of them is blue can be c...

question_answer

Q: Find the solution to the first order differential equation using any acceptable method. (y2+1)dx=yse...

A: Given: The first order differential equation is (y2+1)dx = (ysec2x)dy.The initial condition is y(0)=...

question_answer

Q: 2. (a) Using a Venn diagram, formulate another way to write (A B)UC

A: Let A, B and C are 3 sets. Then, the below figure represents the Venn diagram of (A-B)UC.

question_answer

Q: Prove that if p is a prime, then the square root of p is irrational.

A: Click to see the answer

question_answer

Q: Abstract Algebra (Proof writing): Looking for assistance on this problem please.

A: We claim that Φ is a well defined mapping and that Φ is an isomorphism.Thus we need to check the fol...

question_answer

Q: Show that the field R(i) as a vector space over R has a basis { 1 , i } and is isomorphic to  R_2, w...

A: The field ℝ (i) is defined as ℝ (i) = {a + bi| a, b ϵ ℝ}.That implies, ℝ (i) = {a × 1+ b × i | a, b ...

question_answer

Q: Using the existence and uniqueness theorem for second order linear ordinary differential equations, ...

A: The given initial value problem is:

question_answer

Q: Q- (Subgroup Test for Finite Groups). Let G be a finite group. Prove that a nonempty subset H ⊆ G is...

A: To verify that H is a subgroup , using the finiteness assumption on G.

question_answer

Q: (The party problem). Prove the following: At a party of six people there must exist either three peo...

A: The above problem is known as Friendship Theorem and is an example of a Ramsey theory.              ...