Differential Equations - Initial Value Problem

  • Thread starter mattbonner
  • Start date
  • #1
14
0

Homework Statement



Suppose that the initial value problem
y' = 7(x^2) + (5y^2) − 6, y(0)=−2
has a solution in an interval about x=0.

Find y'(0) =
Find y''(0) =
Find y'''(0) =

Homework Equations



get it into standard form: dy/dt + p(t)y = g(t)
find integrating factor = e^([tex]\int[/tex]p(t)dt + k

multiply everything by integrating factor, simplify left-hand-side and then integrate both sides

using initial condition, solve for C
solve for y

The Attempt at a Solution



i don't seem to be able to get it into standard form

i tried doing y' - 5y^2 = 7x^2 -6
which gave me an integrating factor of e^-5xy

i tried following the rest of the steps with that integrating factor but its not working
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,263
619
You don't actually have to solve the equation to find the derivatives of y(x) at x=0. To find y'(0) just plug x=0, y=(-2) into the equation. To find the higher derivatives, just differentiate the equation with respect to x a couple of times.
 
  • #3
14
0
oh wow i feel like such a moron
thank you so much!!

edit: wait, for y''(0)

i differentiated it, and i got 14x?


edit(2): nvm i solved it
 
Last edited:

Related Threads on Differential Equations - Initial Value Problem

Replies
3
Views
938
Replies
2
Views
1K
Replies
5
Views
4K
Replies
1
Views
5K
Replies
16
Views
3K
Replies
15
Views
639
Replies
9
Views
2K
Replies
4
Views
979
Replies
14
Views
2K
Replies
11
Views
2K
Top