d²y_1 dy _ 4x²y = 0, -∞ < x < 0, y₁ = e²² dx² x 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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Show that given function is a solution of the differential equation. Then solve the equation by finding a general solution.
![The image contains a second-order linear differential equation with variable coefficients. It is expressed as:
\[
\frac{d^2 y}{dx^2} - \frac{1}{x} \frac{dy}{dx} - 4x^2 y = 0,
\]
subject to the condition:
\[
-\infty < x < \infty, \quad y_1 = e^{x^2}
\]
Here, the differential equation is defined over the entire real line (\(-\infty < x < \infty\)), and a particular solution \(y_1 = e^{x^2}\) is given. This kind of differential equation appears in mathematical physics and engineering problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d410cd6-8fc6-4d13-8ff0-7a43ba3056bc%2F548be7ee-ebc5-47dc-9ff2-dcb25d1e9ba5%2Fzftcmfo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains a second-order linear differential equation with variable coefficients. It is expressed as:
\[
\frac{d^2 y}{dx^2} - \frac{1}{x} \frac{dy}{dx} - 4x^2 y = 0,
\]
subject to the condition:
\[
-\infty < x < \infty, \quad y_1 = e^{x^2}
\]
Here, the differential equation is defined over the entire real line (\(-\infty < x < \infty\)), and a particular solution \(y_1 = e^{x^2}\) is given. This kind of differential equation appears in mathematical physics and engineering problems.
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