To solve the separable differential equation we must find two separate integrals: dy= = help (formulas) and d dx help (formulas) The first integral we integrate by substitution: u = help (formulas) du = help (formulas) Solving for y we get one positive solution y = help (formulas) And one negative solution y = ☐ help (formulas) Note: You must simplify all arbitrary constants down to one constant k. Find the particular solution satisfying the initial condition y(x) = = ☐ help (formulas) Book: Section 1.3 of Notes on Diffy Qs dy 1 y² - 6 dx 2y y(1) = −5.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
To solve the separable differential equation
we must find two separate integrals:
dy=
=
help (formulas)
and
d
dx
help (formulas)
The first integral we integrate by substitution:
u =
help (formulas)
du =
help (formulas)
Solving for y we get one positive solution
y =
help (formulas)
And one negative solution
y =
☐ help (formulas)
Note: You must simplify all arbitrary constants down to one constant k.
Find the particular solution satisfying the initial condition
y(x) =
= ☐ help (formulas)
Book: Section 1.3 of Notes on Diffy Qs
dy
1
y² - 6 dx
2y
y(1) = −5.
Transcribed Image Text:To solve the separable differential equation we must find two separate integrals: dy= = help (formulas) and d dx help (formulas) The first integral we integrate by substitution: u = help (formulas) du = help (formulas) Solving for y we get one positive solution y = help (formulas) And one negative solution y = ☐ help (formulas) Note: You must simplify all arbitrary constants down to one constant k. Find the particular solution satisfying the initial condition y(x) = = ☐ help (formulas) Book: Section 1.3 of Notes on Diffy Qs dy 1 y² - 6 dx 2y y(1) = −5.
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