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6_3_Separation_Variables_Homogeneous_Eq

6_3_Separation_Variables_Homogeneous_Eq - 6.3 Separation of...

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Unformatted text preview: 6.3 Separation of Variables & Homogeneous Diff Eq. HW: p. 429 # 131, 39 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: intro (1 of 14) 6.3 Separation of Variables & Homogeneous Diff Eq. Consider: Can we solve? dy/dx = (1/2) xy vs. dy/dx = (1/2) x + y Yes. No. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: intro (2 of 14) 6.3 Separation of Variables & Homogeneous Diff Eq. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: separation of variables (3 of 14) 6.3 Separation of Variables & Homogeneous Diff Eq. Homogeneous Differential Equation where M and N are homogeneous functions of the same degree. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: Homogeneous Diff Eq (4 of 14) 6.3 Separation of Variables & Homogeneous Diff Eq. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: homogeneous eq (5 of 14) 6.3 Separation of Variables & Homogeneous Diff Eq. Yes. Is homogeneous function, but...... No. Not homogeneous diff eq . It needs to fit the form: M(x,y) dx + N(x,y) dy = 0 where M and N are homogeneous to the same degree . Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: homogeneous diff eq (6 of 14) 6.3 Separation of Variables & Homogeneous Diff Eq. degree 1 degree 2 Therefore, NOT a homogeneous differential equation. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: NOT homogeneous (7 of 14) 6.3 Separation of Variables & Homogeneous Diff Eq. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example (8 of 14) 6.3 Separation of Variables & Homogeneous Diff Eq. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example (9 of 14) 6.3 Separation of Variables & Homogeneous Diff Eq. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example (10 of 14) 6.3 Separation of Variables & Homogeneous Diff Eq. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example (11 of 14) 6.3 Separation of Variables & Homogeneous Diff Eq. p.1 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 2 Title: example (12 of 14) 6.3 Separation of Variables & Homogeneous Diff Eq. p.2 previous: Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example (13 of 14) 6.3 Separation of Variables & Homogeneous Diff Eq. p.3 previous: Calculus Home Page Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework Part 1 Homework Part 2 Title: example (14 of 14) ...
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