(xe + sin (3x)) đr +(x'e -2 cos(y))dy = 0. a) Show that the differential equation is exact. b) Find the general solution, ƒ (x,y). c) Find the particular solution if y(0)=r.

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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Based on your understanding, solve the following problem

Given a differential equation,
(re" + sin (3x)) cx +(x’e -2 cos(y))dy = 0.
a) Show that the differential equation is exact.
b) Find the general solution, f (x, y).
c) Find the particular solution if y(0)= r.
Answer:
x'e? 1
S(1.9)=con (0)- 2 in y = -
cos (0)- 2 sin y =-
3
3
Transcribed Image Text:Given a differential equation, (re" + sin (3x)) cx +(x’e -2 cos(y))dy = 0. a) Show that the differential equation is exact. b) Find the general solution, f (x, y). c) Find the particular solution if y(0)= r. Answer: x'e? 1 S(1.9)=con (0)- 2 in y = - cos (0)- 2 sin y =- 3 3
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