condition a) dy - Va,y(4) -0 %3D dx b) dx dy -xVx +9,y(-4) =0 dy c) dx x +1 10 y(0) = 0 %3D

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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**Differential Equations Practice: Find the Function**

**Problem Statement:**

Find a function \( y = f(x) \) satisfying the given differential equation and the prescribed initial condition.

a) \(\dfrac{dy}{dx} = \sqrt{x}, \; y(4) = 0 \)

b) \(\dfrac{dy}{dx} = x\sqrt{x^2 + 9}, \; y(-4) = 0 \)

c) \(\dfrac{dy}{dx} = \dfrac{10}{x^2 + 1}, \; y(0) = 0 \)

No diagrams or graphs are presented in this problem statement. Note the symbolic illustration on the right side representing undefined content.
Transcribed Image Text:**Differential Equations Practice: Find the Function** **Problem Statement:** Find a function \( y = f(x) \) satisfying the given differential equation and the prescribed initial condition. a) \(\dfrac{dy}{dx} = \sqrt{x}, \; y(4) = 0 \) b) \(\dfrac{dy}{dx} = x\sqrt{x^2 + 9}, \; y(-4) = 0 \) c) \(\dfrac{dy}{dx} = \dfrac{10}{x^2 + 1}, \; y(0) = 0 \) No diagrams or graphs are presented in this problem statement. Note the symbolic illustration on the right side representing undefined content.
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