3. = 4x³y-y, y(1) = -3 (Solve the DE using separation of variables and linear order differential equation.) 12

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Answer 1,2 and 3 only

E. Use separation of variables or linear differential equations to solve the following differential equations
or initial value problems.
1. ey- =e=y+e=2x-y
dy
dx
2.
dy
dr
=
xy - 2x + 4y - 8
2xy + x2y1
dy
3. = 4x³y-y, y(1) = −3 (Solve the DE using separation of variables and linear order differential
d.x
equation.)
4. (x²+4)y + 3xy = Use trigonometric substitution for the indefinite integral of the integrating
factor multiplied by the right side of the standard form of this given linear DE.
X
5. ydx = (2y² + x)dy
6. (continuous solution)
dy
+ P(x)y = 4x where P(x) =
2 if 0≤x≤ 1
2
HIN
if x ≥ 1
,y(0) = 3
Transcribed Image Text:E. Use separation of variables or linear differential equations to solve the following differential equations or initial value problems. 1. ey- =e=y+e=2x-y dy dx 2. dy dr = xy - 2x + 4y - 8 2xy + x2y1 dy 3. = 4x³y-y, y(1) = −3 (Solve the DE using separation of variables and linear order differential d.x equation.) 4. (x²+4)y + 3xy = Use trigonometric substitution for the indefinite integral of the integrating factor multiplied by the right side of the standard form of this given linear DE. X 5. ydx = (2y² + x)dy 6. (continuous solution) dy + P(x)y = 4x where P(x) = 2 if 0≤x≤ 1 2 HIN if x ≥ 1 ,y(0) = 3
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