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Consider the so called Riccati ODE and let y₁ be a solution. y' = p(t)y² + q(t)y + g(t). Show that: a. The transform 1 y = y₁ + Z turns the ODE into a first order linear ODE with respect to z. b. The transform y = y₁ + z turns the ODE into a Bernoulli ODE with respect to z.

Consider the so called Riccati ODE and let y₁ be a solution. y' = p(t)y² + q(t)y + g(t). Show that: a. The transform 1 y = y₁ + Z turns the ODE into a first order linear ODE with respect to z. b. The transform y = y₁ + z turns the ODE into a Bernoulli ODE with respect to z.

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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Ordinary differential equation

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Consider the so called Riccati ODE and let y₁ be a solution. y' = p(t)y² + q(t)y + g(t). Show that: a. The transform 1 y = y₁+ Z turns the ODE into a first order linear ODE with respect to z. b. The transform Y=Y₁+z turns the ODE into a Bernoulli ODE with respect to z.
Transcribed Image Text:Consider the so called Riccati ODE and let y₁ be a solution. y' = p(t)y² + q(t)y + g(t). Show that: a. The transform 1 y = y₁+ Z turns the ODE into a first order linear ODE with respect to z. b. The transform Y=Y₁+z turns the ODE into a Bernoulli ODE with respect to z.
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