Lecture18 Differential Equation of the first order and higher degree UG BSc Part2 Dr Md Ataur Rahman Guest Faculty Department of Mathematics M L Arya College Kasba ID: 1002930
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1. Differential Equation Lecture-18 Differential Equation of the first order and higher degreeUG (B.Sc., Part-2)Dr. Md. Ataur RahmanGuest FacultyDepartment of MathematicsM. L. Arya, College, KasbaPURNEA UNIVERSITY, PURNIA
2. ContentsDifferential equation of the first order but not of the first degreeThe general form of differential equation of the first order but not of the first degreei.e. the general form of differential equation of the first order and higher degree. Solution of the first order and higher degree D.E.
3. Differential equation of the first order but not of the first degreeThe general form of a differential equation of the first order and nth degree is
4. Solution of the first order and higher degree D.E.Methods of solving such types of differential equationsEquations Solvable for pEquations Solvable for yEquations Solvable for x
5. 1. Equations Solvable for pLet the general form of the differential equation of the first order and nth degree beWorking rule:- Factorize (1) into n linear factorsi.e.Equating each factor of (2) to zero, we get
6. ContinueAfter integrating ,We getThen the general solution of (1) isSince the equation (1) is the first order differential equation.So, the general solution of (1) contains only one arbitrary constant.
7. ProblemsSolve the following differential equations
8. Solution Solution (1):- Given equation is
9. Continue Integrating it, we getThen the general solution of (1) is