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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09b1a8e5-9655-45e9-a4fb-903c7d32b996%2Fdd66be32-c496-4080-aab4-66a45d105e24%2Fr2avf9e_processed.jpeg&w=3840&q=75)
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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