Solution Found!
(a) Show that y2 + x – 3 = 0 is an implicit solution to
Chapter 1, Problem 1E(choose chapter or problem)
\(\frac{d y}{d x}=\frac{(x \cos x+\sin x-1) y}{3(x-x \sin x)}\)
on the interval \((0, \pi / 2)\)
Equation Transcription:
Text Transcription:
y^2+x-3=0
dy/dx=-1/(2y)
(-infinity,3)
xy^3-xy^3sin x=1
dy over dx=(x cos x+sin x-1)y over 3(x-x sin x)
(0,pi/2)
Questions & Answers
QUESTION: Show that \(y^{2}+x-3=0\) is an implicit solution to \(d y / d x=-1 /(2 y)\) on the interval \((-\infty, 3)\).Show that \(x y^{3}-x y^{3} \sin x=1\) is an implicit solution to
\(\frac{d y}{d x}=\frac{(x \cos x+\sin x-1) y}{3(x-x \sin x)}\)
on the interval \((0, \pi / 2)\)
Equation Transcription:
Text Transcription:
y^2+x-3=0
dy/dx=-1/(2y)
(-infinity,3)
xy^3-xy^3sin x=1
dy over dx=(x cos x+sin x-1)y over 3(x-x sin x)
(0,pi/2)
ANSWER:
SOLUTION
Step 1
In this problem, we are asked to show the following