Differential Equation

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Presentation transcript:

Differential Equation Prof. Suvarna Bhagwat Assistant Professor Department of Applied Sciences & Engineering Hope Foundation’s International Institute of Information Technology, I²IT

ORDER & DEGREE ORDER OF DIFFERENTIAL EQUATION Definition: Order of differential equation is the order of highest order derivative in differential equation. Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

Order of highest order derivative =2 Order of differential equation=2 Example: Order of highest order derivative =2 Order of differential equation=2 Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

DEGREE OF DIFFERENTIAL EQUATION Definition: The degree of differential equation is the degree of highest order derivative free from radicals and fractions. Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

Degree of highest order derivative =1 Example: Degree of highest order derivative =1 Degree of differential equation=1 Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

Exercise: Find the order & degree of differential equation Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

FORMATION OF DIFFERENTIAL EQUATION FROM GENERAL SOLUTION 1. If general solution contains ‘n’ no. of constants then differentiate equation ‘n’ no. of times. (No.of differentiation = No.of arbitraray constants) 2.Elliminate the arbitrary constants. Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

Example Form the differential equation whose general solution is Sol. Given Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

For details, please contact Suvarna Bhagwat suvarnab@isquareit.edu.in Department of Applied Sciences & Engineering Hope Foundation’s International Institute of Information Technology, I²IT P-14,Rajiv Gandhi Infotech Park MIDC Phase 1, Hinjawadi, Pune – 411057 Tel - +91 20 22933441/2/3 www.isquareit.edu.in | info@isquareit.edu.in