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# classification of second order partial differential equation

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classification of second order partial differential equation

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### classification of second order partial differential equation

1. 1. Active learning Assignment Topic : CLASSIFICATION OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATION BRANCH : ELECTRICAL ENGINEERING BATCH : B1 SUBJECT : ADVANCED ENGINEERING MATHEMATICS Prepared By : JIGAR METHANIYA(150120109021) Guided By : Prof. MIHIR SUTHAR 1
2. 2. β’ The general form of a non Homogeneous second order P.D.E is β’ π΄ π₯, π¦ π2 π’ ππ₯2+B π₯, π¦ π2 π’ ππ₯ππ¦ +C π₯, π¦ π2 π’ ππ¦2+f π₯, π¦, π’, ππ’ ππ₯ , ππ’ ππ¦ =F π₯, π¦ β¦β¦β¦..(1) β’ Equation (1) is said to be β’ Elliptic , if π΅2 -4AC < 0 β’ Parabolic , if π΅2 -4AC = 0 β’ Hyperbolic , if π΅2-4AC > 0 β’ CLASSIFICATION OF SECOND-ORDER PARTIAL DIFFERENTIAL EQUATION
3. 3. β’ EXAMPLE:-1 Classify the Following P.D.E ππ’ ππ‘ = π2 π’ ππ₯2 Ans:- Comparing this equation with (1) we get A=1 , B=0 , C=0 So , π΅2 -4AC = 0 Hence given P.D.E. is parabolic.
4. 4. β’ EXAMPLE:-2 Classify the following P.D.E π2 π’ ππ₯2 + π2 π’ ππ¦2=0 Ans:- Comparing this given P.D.E with (1) we get A=C=1 , B=0 So , π΅2-4AC = -4<0 Hence , given P.D.E is elliptic.
5. 5. β’ EXAMPLE:- 3 Classify the Following P.D.E π2 π’ ππ₯2 + 3 π2 π’ ππ₯ππ‘ + π2 π’ ππ‘2 =0 Ans:- Comparing this given P.D.E with (1) we get A=1 , B=3 , C=1 So , π΅2 -4AC = 9-4 = 5>0 Hence the given P.D.E is hyperbolic.