B. Homogeneous 1. у(x+ ху - 2у?) dx + x(3у? — ху- х?) dy 3D0 2. (x+y sin 2) dx -x sin dy = 0 3. xy dx + 2(x? + 2y?) dy = 0; x = 0, y = 1 4. y(x? + y') dx + x(3x? - 5y) dy = 0; x =2, 2y-2y'x? + 3x = 0 y = C sin ? Y =x sin (C-In x) In x + cos = C y=1 y3 2y? In+2xy + x² = Cy y'(3x? + 4y) = 4 5. xy' = y- Vx2 - y?
B. Homogeneous 1. у(x+ ху - 2у?) dx + x(3у? — ху- х?) dy 3D0 2. (x+y sin 2) dx -x sin dy = 0 3. xy dx + 2(x? + 2y?) dy = 0; x = 0, y = 1 4. y(x? + y') dx + x(3x? - 5y) dy = 0; x =2, 2y-2y'x? + 3x = 0 y = C sin ? Y =x sin (C-In x) In x + cos = C y=1 y3 2y? In+2xy + x² = Cy y'(3x? + 4y) = 4 5. xy' = y- Vx2 - y?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Equations and inequalities describe the relationship between two mathematical expressions.
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Solve the items 1-3, show your complete solution.
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