Solve the following equations for exactness, then solve: 1. ( cos 2y - 3x2y2) dx + (cos 2y - 2x sin 2y - 2x3y) dy = 0
Solve the following equations for exactness, then solve: 1. ( cos 2y - 3x2y2) dx + (cos 2y - 2x sin 2y - 2x3y) dy = 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Exact Differentail Equation
M (x,y) dx + N (x,y) dy = 0 is an Exact DE
when ∂M/∂y = ∂N/∂x
Solution steps Method II
a. Same as in ia.
b. Differentiate F with respect to y, x as constant; then equate to N.
dF/dy = d/dy[∫M dx] + dg(y)/dy = N
c. Solve for g(y)
d. Substitute g(y) into F equation in (a) to get the General Solution.
Solve the following equations for exactness, then solve:
1. ( cos 2y - 3x2y2) dx + (cos 2y - 2x sin 2y - 2x3y) dy = 0
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