{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

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

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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 .
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

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 ....
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern