7. Solve the equation Y'(t) = XY (t) + = 1 1 + t² Y(0) = 0; Y(t) = tan-¹(t) is the true solution. Use Euler's method, the backward Euler method, and the trapezoidal method. Let A : -1,-10, -50, and h = 0.5, 0.1, 0.001. Discuss the results. In implementing the backward Euler method and the trapezoidal method, note that the implicit equation for yn+1 can be solved explicitly without iteration. - A tan-¹(t),

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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7. Solve the equation
=
1
1 + t²
Y'(t) = XY (t) +
Y(0) = 0;
Y(t)
tan−¹(t) is the true solution. Use Euler's method, the backward
Euler method, and the trapezoidal method. Let A -1,-10, −50, and
h = 0.5, 0.1, 0.001. Discuss the results. In implementing the backward Euler
method and the trapezoidal method, note that the implicit equation for yn+1
can be solved explicitly without iteration.
· A tan¯¹(t),
-
Transcribed Image Text:7. Solve the equation = 1 1 + t² Y'(t) = XY (t) + Y(0) = 0; Y(t) tan−¹(t) is the true solution. Use Euler's method, the backward Euler method, and the trapezoidal method. Let A -1,-10, −50, and h = 0.5, 0.1, 0.001. Discuss the results. In implementing the backward Euler method and the trapezoidal method, note that the implicit equation for yn+1 can be solved explicitly without iteration. · A tan¯¹(t), -
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