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MATH24 Non-exact DE (Q1) - linear equation of order one

# MATH24 Non-exact DE (Q1) - linear equation of order one -...

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Consider the General Form of DE M(x,y) dx + N(x,y) dy = 0 ––––––––– (1) where . To transform (1) into an exact equation, multiply it by an integrating factor,(lambda). Non - Exact differential equations may be solved using any of the five methods as applicable: 1. Reducing it to Linear Equation of Order One 2. Transforming to Bernoulli’s Equation 3. Integrating Factor by Inspection 4. Integrating Factor found by Formula (Partial Differentiation) 5. Miscellaneous Substitutions 1. Reducing to Linear Equation of Order One INTEGRATING FACTOR OF A LINEAR D.E. Multiply both sides by an integrating factor v(x). Combine the coefficients of dx. Bearing in mind that v, P and Q are functions of x, then for an equation that is linear in y if the equation is linear in x General Solution: Multiply both sides by .

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Unformatted text preview: Integrating both sides will yield the general solution if the equation is linear in y if the equation is linear in x If the given equation is not exact, reduce it to either form listed below and find an integrating factor,: Linear in y: dy + y P(x) dx = Q(x) dx G.S.: Linear in x: dx + x P(y) dy = S(y) dy Examples: Find the general solution of the differential equation. 1. Ans: 2. Ans: 3. Ans: 4. Ans: 5. Ans: 6. Ans: 7. Ans: 8. Ans: 9. Ans: From Rainville (page 39): #8. . #14. , where and are constants. #16. . #22. . #24. ; , , are constants with , . #25. Solve the equation of Exercise 24 for the exceptional cases and . #28. ; when , . #30. ; where , , and are constants, when , . #32. Find that solution of which passes through the point ....
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