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
Example: 2
d y y 0 2 dx 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
Example:
2
d y y 0 2 dx 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 dy x 2 y 3 1. dx x y 1
2 d y dy 2 2. x x ny 2 dx dx 2
2
d y dy 3 .1 0 2 dx dx 3
d y dy 4 . 3 y 2 dx dx 2
2
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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 2x 3x general solution is y a e b e . Sol. Given 2x 3x n y a e b e eq .1
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No.of arbitraryconstant 2 Differentiating w.r.t.x, we have y1 2 ae2 x 3be3x eqn .2 Againdifferentiatingw.r.to x y2 4ae2 x 9be3x eqn .3
Usingequation1,2,3elliminating arbitraryconstants y2 5 y1 6 y 0 requireddifferential 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
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