The substitution y = xv(x) transforms a homogeneous equation into a separable equation. The latter equation can be solved by direct integration, and then replacing v by gives the solution to the y X original equation. Use this method to solve the differential equation NOTE: Use c for the constant of integration. y(x) = ±x√√x³-1 X dy x² +21y² 20xy dx =
The substitution y = xv(x) transforms a homogeneous equation into a separable equation. The latter equation can be solved by direct integration, and then replacing v by gives the solution to the y X original equation. Use this method to solve the differential equation NOTE: Use c for the constant of integration. y(x) = ±x√√x³-1 X dy x² +21y² 20xy dx =
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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Question
![The substitution y = xv(x) transforms a homogeneous equation into a
separable equation. The latter equation can be solved by direct
integration, and then replacing v by gives the solution to the
Y
X
original equation.
Use this method to solve the differential equation
NOTE: Use c for the constant of integration.
y(x) = ± √x-1
X
X
dy x² + 21y²
=
dx 20xy](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5b87728-ae8f-4b34-9b04-2eb269cb5823%2F505b006c-4a7d-4c7e-8cf7-a6d7bbbfefa7%2Fzj2jm5t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The substitution y = xv(x) transforms a homogeneous equation into a
separable equation. The latter equation can be solved by direct
integration, and then replacing v by gives the solution to the
Y
X
original equation.
Use this method to solve the differential equation
NOTE: Use c for the constant of integration.
y(x) = ± √x-1
X
X
dy x² + 21y²
=
dx 20xy
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