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Solve by simple substitution. 1. xy²(xdy + ydx) = (xy-2)dy

Solve by simple substitution. 1. xy²(xdy + ydx) = (xy-2)dy

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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Answer the question, use EXAMPLE 2 as reference and guide.
Solve the solution of xy (xdy + ydx) = 6y³dy Example 2: Solution: The presence of xy and its differential, xdy + ydx leads us to put z = xy And dz = xdy + ydx Substituting these in the given differential equation: zdz = 6y³dy The result is a differential equation involving z and y only, and whose variables are already separated. Integrating term by term: 1 6y* = +C 2 Clearing of fractions: or 2z² = 6y² + 4C z² = 3y² + 2C z² = 3y² + C₁ variables, we have: (xy)² = 3y² + C₁ Restoring the original or just simply x²y² = 3y4+C ⇒ General solution
Transcribed Image Text:Solve the solution of xy (xdy + ydx) = 6y³dy Example 2: Solution: The presence of xy and its differential, xdy + ydx leads us to put z = xy And dz = xdy + ydx Substituting these in the given differential equation: zdz = 6y³dy The result is a differential equation involving z and y only, and whose variables are already separated. Integrating term by term: 1 6y* = +C 2 Clearing of fractions: or 2z² = 6y² + 4C z² = 3y² + 2C z² = 3y² + C₁ variables, we have: (xy)² = 3y² + C₁ Restoring the original or just simply x²y² = 3y4+C ⇒ General solution
Solve by simple substitution. 1. xy²(xdy + ydx) = (xy-2)dy
Transcribed Image Text:Solve by simple substitution. 1. xy²(xdy + ydx) = (xy-2)dy
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