3. Given f"(x) = x² + sin(2x): (a) If f(0) = 2, f'(0) = 1, find f'(x) and f(x) (HINT: Python does NOT include the "+C" when you use integrate, so you have to put it in yourself, then use the initial conditions to find each C. This type of problem is called an initial value problem) (b) If ƒ(0) = f(7) = 1, find f(x) (Notice this time you cannot solve for the C values until the end, so give them different names, like C1 and C2, then solve a system of equations for them. This type of problem is called a boundary value problem)

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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3. Given f"(x) = x² + sin(2x):
(a) If f(0) = 2, f'(0) = 1, find f'(x) and f(x)
(HINT: Python does NOT include the "+C" when you use integrate, so
you have to put it in yourself, then use the initial conditions to find each C.
This type of problem is called an initial value problem)
(b) If f(0) = f (#) = 1, find f (x)
(Notice this time you cannot solve for the C values until the end, so give
them different names, like C1 and C2, then solve a system of equations for
them. This type of problem is called a boundary value problem)
Transcribed Image Text:3. Given f"(x) = x² + sin(2x): (a) If f(0) = 2, f'(0) = 1, find f'(x) and f(x) (HINT: Python does NOT include the "+C" when you use integrate, so you have to put it in yourself, then use the initial conditions to find each C. This type of problem is called an initial value problem) (b) If f(0) = f (#) = 1, find f (x) (Notice this time you cannot solve for the C values until the end, so give them different names, like C1 and C2, then solve a system of equations for them. This type of problem is called a boundary value problem)
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