100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
DIFFERENTIAL EQUATIONS STUDY QUESTIONS WITH COMPLETE SOLUTIONS GRADED A+ $13.19   Add to cart

Exam (elaborations)

DIFFERENTIAL EQUATIONS STUDY QUESTIONS WITH COMPLETE SOLUTIONS GRADED A+

 1 view  0 purchase
  • Course
  • DIFFERENTIAL EQUATIONS
  • Institution
  • DIFFERENTIAL EQUATIONS

DIFFERENTIAL EQUATIONS STUDY QUESTIONS WITH COMPLETE SOLUTIONS GRADED A+ What is the existence and uniqueness thm for non linear DEs? - Answer-Let f(t,y) and partial[f(t,y)]/partial y be continuous on some rectangular region a < t < b, c < y < d. Let (t0, y0) be a point in the rectang...

[Show more]

Preview 1 out of 4  pages

  • October 23, 2024
  • 4
  • 2024/2025
  • Exam (elaborations)
  • Questions & answers
  • DIFFERENTIAL EQUATIONS
  • DIFFERENTIAL EQUATIONS
avatar-seller
victoryguide
DIFFERENTIAL EQUATIONS STUDY
QUESTIONS WITH COMPLETE
SOLUTIONS GRADED A+
What is the existence and uniqueness thm for non linear DEs? - Answer-Let f(t,y) and
partial[f(t,y)]/partial y be continuous on some rectangular region a < t < b, c < y < d.
Let (t0, y0) be a point in the rectangular region a < t < b, c < y < d
Then there exists an h > 0 such that the initial value problem
y' + p(t) y = q(t)
y(t0) = y0
has a unique solution y = f(t) defined on the interval t0-h < t < t0+h

When is a DE separable? - Answer-When the variables of the equation can be
separated to different sides of the equation. f(t,y) = g(t)/h(y) or f(t,y) = g(t) h(y) which can
be rewritten as g(t) dt = h(y) dy

What is the difference between ODEs and PDEs? - Answer-If there are any partial
derivatives, then the equation is a partial differential equation. If there is more than one
independent variable, then the equation is a partial differential equation.

What is a Linear DE? - Answer-Ay'+Bxy=0 is linear in the variable y.

First order linear equations have what form? - Answer-P(t)y' + Q(t)y = G(t)

Integrating Factor for First Order Linear Eqs - Answer-Consider the function µ(t) =
e^∫p(t)dt
d(µ(t))/dt = p(t) * µ(t)
so µ'(t) = p(t)µ(t) when µ(t) = e^∫p(t)dt
Integrating Factor is e^∫p(t)dt

Find the independent and dependent variables: f(x, y', y'', y'''). - Answer-x is the
independent variable, y is the dependent variable

How do we study Dif Eqs? - Answer-Analytically: We find an explicit or implicit function y
that satisfies the dif eq.
Numerically: Approximate the values of the solution at certain points.
Visually: Sketch solutions (integral curves) and create a slope(direction) field.

What we mean by y is a solution to the DE y' = f(t,y) on some interval (a,b)? - Answer-y
is a solution to a DE if:
1) y is differentiable on the interval (a,b)
2) y satisfies the equation y'=f(t,y)

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller victoryguide. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $13.19. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

82871 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$13.19
  • (0)
  Add to cart