3. Given that y₁ = t−¹ is a solution of 2t²y" + 3ty' — y=0, t>0, a) Substitute y = v(t)y₁(t) into the differential equation and simplify.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 15CR
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3. Given that y₁ = t-¹ is a solution of
2t²y" + 3ty' — y=0, t>0,
a) Substitute y = v(t)y₁(t) into the differential equation and simplify.
b) Rewrite the result from a with w = = v' (t).
Solve the rewritten equation for w.
d) Solve the substitution w = v'(t) for v, and give the general solution.
Transcribed Image Text:3. Given that y₁ = t-¹ is a solution of 2t²y" + 3ty' — y=0, t>0, a) Substitute y = v(t)y₁(t) into the differential equation and simplify. b) Rewrite the result from a with w = = v' (t). Solve the rewritten equation for w. d) Solve the substitution w = v'(t) for v, and give the general solution.
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ISBN:
9780321964038
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