The value of k so that (y³ +kxy“ –2x)dx-(3xy? + 20x?y³ )dy = Ois an exact equation2,3+is:а. 10С. -5b. 5d. 15

A differential equation of the form Mdx+Ndy=0 is said to be exact if ∂M∂y=∂N∂x

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The value of k so that (y³ +kxy* – 2x)dx + (3xy? +20x?y³ )dy = 0is an exact equa is: а. 10 С. -5 b. 5 d. 15

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section: Chapter Questions

Problem 48RE

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Question

The value of k so that (y³ +kxy“ –2x)dx-
(3xy? + 20x?y³ )dy = Ois an exact equation
2,3
+
is:
а. 10
С. -5
b. 5
d. 15

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By expanding (xh)2+(yk)2=r2, we obtain x22hx+h22ky+k2r2=0. When we compare this result to the form x2+y2+Dx+Ey+F=0, we see that D=2h,E=2k, and F=h2+k2r2. Therefore, the center and the length of a radius of a circle can be found by using h=D2,k=E2 and r=h2+k2F. Use these relationship to find the center and the length of the radius of each of the following circles. x2+y2+4x14y+49=0

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