Consider the following Initial Value Problems (IVPs). dy dt dy ● dt dy dr dy dt + 2ty = te-t², y(0) = 1. y(0) = 0. y(0) = 0. 1=2, ry, = = 2t - 3y, -10 y(0)= 7 9 (a) The slope fields of some of the IVPs are given below. Match each IVP with its slope field. Sketch the missing slope field. 10+ 10 (b) Identify the IVPs that can be solved by using "integrating factor" method. Find the exact solution to each of the IVPs you have identified.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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1. Consider the following Initial Value Problems (IVPS).
dy
dt
dy
dt
dy
dr
dy
dt
+2ty=te-t². y(0) = 1.
y(0) = 0.
y (0) = 0.
y = 2,
√IY,
= 2t - 3y,
y(0) =
7
9
(a) The slope fields of some of the IVPS are given below. Match each IVP with its slope field. Sketch
the missing slope field.
10
(b) Identify the IVPs that can be solved by using "integrating factor" method. Find the exact solution
to each of the IVPS you have identified.
(c) Use Euler's method to approximate the solution to each of the given IVPs on the interval [0, 3] with
step size h = 0.5.
10
Transcribed Image Text:1. Consider the following Initial Value Problems (IVPS). dy dt dy dt dy dr dy dt +2ty=te-t². y(0) = 1. y(0) = 0. y (0) = 0. y = 2, √IY, = 2t - 3y, y(0) = 7 9 (a) The slope fields of some of the IVPS are given below. Match each IVP with its slope field. Sketch the missing slope field. 10 (b) Identify the IVPs that can be solved by using "integrating factor" method. Find the exact solution to each of the IVPS you have identified. (c) Use Euler's method to approximate the solution to each of the given IVPs on the interval [0, 3] with step size h = 0.5. 10
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