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Elimination of arbitrary constants 1. 72 1. x == c(x² - y²) 2. 3. II. 1. 12 2. III. 3. y= = C C₁cos2x + C₂sin2x -2x y = (C₁ + C₂x)e + C₁₂ Separation of Variables ylnx lny dx dy = 0 xdx + sqrt of (a-xdy = 0 Homogeneous Differential Equation 2) 3xy dx+(x²-ydy = 0 2) ydx + xy dy = 0 y²dx + (x²+3xy+4y²)dy = 0 Exact Equations 2) (6x² + y² dx + (2x-3y)dy = 0 312 1. (x - 2. ≥123 IV. 1. 2. 3. 772 V. 1. 2. (xy²+x - 2y+3)dx + x²y dy = 2(x + y)dy, when x = 1, y = 1 (2xy + y)dx+(x-x)dy = 0 Linear Order ydx + ( 3x - xy+2)dy = 0 (y-(cosx)^2)dx+ cosxdy = 0

Elimination of arbitrary constants 1. 72 1. x == c(x² - y²) 2. 3. II. 1. 12 2. III. 3. y= = C C₁cos2x + C₂sin2x -2x y = (C₁ + C₂x)e + C₁₂ Separation of Variables ylnx lny dx dy = 0 xdx + sqrt of (a-xdy = 0 Homogeneous Differential Equation 2) 3xy dx+(x²-ydy = 0 2) ydx + xy dy = 0 y²dx + (x²+3xy+4y²)dy = 0 Exact Equations 2) (6x² + y² dx + (2x-3y)dy = 0 312 1. (x - 2. ≥123 IV. 1. 2. 3. 772 V. 1. 2. (xy²+x - 2y+3)dx + x²y dy = 2(x + y)dy, when x = 1, y = 1 (2xy + y)dx+(x-x)dy = 0 Linear Order ydx + ( 3x - xy+2)dy = 0 (y-(cosx)^2)dx+ cosxdy = 0

Advanced Engineering Mathematics
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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kindly answer the differential equations according to the specific given

Elimination of arbitrary constants 1. 72 1. x == c(x² - y²) 2. 3. II. 1. 12 2. III. 3. y= = C C₁cos2x + C₂sin2x -2x y = (C₁ + C₂x)e + C₁₂ Separation of Variables ylnx lny dx dy = 0 xdx + sqrt of (a-xdy = 0 Homogeneous Differential Equation 2) 3xy dx+(x²-ydy = 0 2) ydx + xy dy = 0 y²dx + (x²+3xy+4y²)dy = 0 Exact Equations 2) (6x² + y² dx + (2x-3y)dy = 0 312 1. (x - 2. ≥123 IV. 1. 2. 3. 772 V. 1. 2. (xy²+x - 2y+3)dx + x²y dy = 2(x + y)dy, when x = 1, y = 1 (2xy + y)dx+(x-x)dy = 0 Linear Order ydx + ( 3x - xy+2)dy = 0 (y-(cosx)^2)dx+ cosxdy = 0
Transcribed Image Text:Elimination of arbitrary constants 1. 72 1. x == c(x² - y²) 2. 3. II. 1. 12 2. III. 3. y= = C C₁cos2x + C₂sin2x -2x y = (C₁ + C₂x)e + C₁₂ Separation of Variables ylnx lny dx dy = 0 xdx + sqrt of (a-xdy = 0 Homogeneous Differential Equation 2) 3xy dx+(x²-ydy = 0 2) ydx + xy dy = 0 y²dx + (x²+3xy+4y²)dy = 0 Exact Equations 2) (6x² + y² dx + (2x-3y)dy = 0 312 1. (x - 2. ≥123 IV. 1. 2. 3. 772 V. 1. 2. (xy²+x - 2y+3)dx + x²y dy = 2(x + y)dy, when x = 1, y = 1 (2xy + y)dx+(x-x)dy = 0 Linear Order ydx + ( 3x - xy+2)dy = 0 (y-(cosx)^2)dx+ cosxdy = 0
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