Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 34CR
Related questions
Question
![Question 1. Find the solution of the following differential equations
(i) cos² r sin 2+ (cos³x)y = 1
(ii) y-2xy = 1, y(1) = 1 (Revise Fundamental theorem of Calculus and see definition for erf(x)),
(iii) y¹/2+³/2 = 1, y(1) = 1/
(iv) x=yer/v- x
(v) eye-y+e-22-y
Question 2. Determine a region of the xy-plane for which the given differential equation would
have a unique solution whose graph passes through a point (zo, yo) in the region.
(i) = y2/3
(ii)=√√ry
Question 3. Discuss the existence and uniqueness of a solution of the initial value problem,
(a) xy - 4y = xe", for
(i) y(0) = 0,
(ii) y(ro) yo, 20 > 0, yo > 0.
=
(b) = y, y(0) = 0.
Question 4. Find function M(x, y) so that the given differential equation is exact
M(x,y)dr+(new.
Solve the obtained exact differential equation.
-1) dy
+ 2xy +
dy = 0,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c382931-a364-4965-b162-62b7895a42e8%2Fed6154e3-515a-405c-bb02-2c9ce87768e4%2Fz6r1li_processed.png&w=3840&q=75)
Transcribed Image Text:Question 1. Find the solution of the following differential equations
(i) cos² r sin 2+ (cos³x)y = 1
(ii) y-2xy = 1, y(1) = 1 (Revise Fundamental theorem of Calculus and see definition for erf(x)),
(iii) y¹/2+³/2 = 1, y(1) = 1/
(iv) x=yer/v- x
(v) eye-y+e-22-y
Question 2. Determine a region of the xy-plane for which the given differential equation would
have a unique solution whose graph passes through a point (zo, yo) in the region.
(i) = y2/3
(ii)=√√ry
Question 3. Discuss the existence and uniqueness of a solution of the initial value problem,
(a) xy - 4y = xe", for
(i) y(0) = 0,
(ii) y(ro) yo, 20 > 0, yo > 0.
=
(b) = y, y(0) = 0.
Question 4. Find function M(x, y) so that the given differential equation is exact
M(x,y)dr+(new.
Solve the obtained exact differential equation.
-1) dy
+ 2xy +
dy = 0,
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