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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. ( 3+ y + 2y2 sin2x) dx + ( x + 2xy - y sin2x) dy = 0

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. ( 3+ y + 2y2 sin2x) dx + ( x + 2xy - y sin2x) dy = 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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. ( 3+ y + 2y2 sin2x) dx + ( x + 2xy - y sin2x) dy = 0

 

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