Use the method above to solve the differential equation ty" – 2ty + 2y = 5t2, t > 0, y1(t) = t. NOTE: Use C1, C2, for the constants of integration. ... y(t) =
Use the method above to solve the differential equation ty" – 2ty + 2y = 5t2, t > 0, y1(t) = t. NOTE: Use C1, C2, for the constants of integration. ... y(t) =
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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Transcribed Image Text:The method of reduction of order (Section 3.4) can also be used for
the nonhomogeneous equation
3y" + p(t)y/ + q(t)y = g(t),
provided one solution y1 of the corresponding homogeneous equation
is known. Let y = v(t)y1(t) and show that y satisfies equation 38 if v
(38)
is a solution of
Y1(t)v" + (2y4 (t) + p(t)y1(t))v' = g(t).
(39)
Equation 39 is a first order linear equation for v'. Solving this
equation, integrating the result, and then multiplying by y1(t) leads
to the general solution of the first equation.
Use the method above to solve the differential equation
ty" – 2ty + 2y = 5t², t > 0, yı(t) = t.
NOTE: Use c1, C2,
for the constants of integration.
...
y(t) =
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