Differential Equation Lecture18 Differential Equation of the first

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Differential Equation Lecture-18 Differential Equation of the first order and higher degree UG (B.

Differential Equation Lecture-18 Differential Equation of the first order and higher degree UG (B. Sc. , Part-2) Dr. Md. Ataur Rahman Guest Faculty Department of Mathematics M. L. Arya, College, Kasba PURNEA UNIVERSITY, PURNIA

Contents • Differential equation of the first order but not of the first degree

Contents • Differential equation of the first order but not of the first degree • The general form of differential equation of the first order but not of the first degree • i. e. the general form of differential equation of the first order and higher degree. • Solution of the first order and higher degree D. E.

Differential equation of the first order but not of the first degree The general

Differential equation of the first order but not of the first degree The general form of a differential equation of the first order and nth degree is

Solution of the first order and higher degree D. E. Methods of solving such

Solution of the first order and higher degree D. E. Methods of solving such types of differential equations 1. Equations Solvable for p 2. Equations Solvable for y 3. Equations Solvable for x

1. Equations Solvable for p Let the general form of the differential equation of

1. Equations Solvable for p Let the general form of the differential equation of the first order and nth degree be Working rule: - Factorize (1) into n linear factors i. e. Equating each factor of (2) to zero, we get

Continue After integrating , We get Then the general solution of (1) is Since

Continue After integrating , We get Then the general solution of (1) is Since the equation (1) is the first order differential equation. So, the general solution of (1) contains only one arbitrary constant.

Problems Solve the following differential equations

Problems Solve the following differential equations

Solution (1): - Given equation is

Solution (1): - Given equation is

Continue Integrating it, we get Then the general solution of (1) is

Continue Integrating it, we get Then the general solution of (1) is

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