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4. Determine if the equation is exact, and if it is exact, find the general solution. a.) (y² + 2t) + 2tyy' = 0 b.) 2t? – y + (t+ y²)y/ = 0 c.) 2xy + 2x³ + (x² – y)y' = 0

4. Determine if the equation is exact, and if it is exact, find the general solution. a.) (y² + 2t) + 2tyy' = 0 b.) 2t? – y + (t+ y²)y/ = 0 c.) 2xy + 2x³ + (x² – y)y' = 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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4. Determine if the equation is exact, and if it is exact, find the general solution. a.) (y² + 2t) + 2tyy' = 0 b.) 2t? – y + (t+ y²)y/ = 0 с.) 2.гу + 2л3 + (а2 — у)у — 0 d.) 2ty + (ť² + 3y²)y' = 0, y(1) = 1 e.) Find the conditions on the constants a, b, c, d which guarantee that the differential equation (at + by) = (ct + dy)y is exact.
Transcribed Image Text:4. Determine if the equation is exact, and if it is exact, find the general solution. a.) (y² + 2t) + 2tyy' = 0 b.) 2t? – y + (t+ y²)y/ = 0 с.) 2.гу + 2л3 + (а2 — у)у — 0 d.) 2ty + (ť² + 3y²)y' = 0, y(1) = 1 e.) Find the conditions on the constants a, b, c, d which guarantee that the differential equation (at + by) = (ct + dy)y is exact.
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