Question

A. Let g(t) be the solution of the initial value problem 6t dy/dt + y = 0, t > 0, with g(1) = 1. Find g(t). g(t) = t^(-1/6) B. Let f(t) be the solution of the initial value problem 6t dy/dt + y = t^4 with f(0) = 0. Find f(t). f(t) = t^(4/17) C. Find a constant c so that k(t) = f(t) + cg(t) solves the differential equation in part B and k(1) = 4. c = 6

          A. Let g(t) be the solution of the initial value problem
6t dy/dt + y = 0, t > 0,
with g(1) = 1.
Find g(t).
g(t) = t^(-1/6)

B. Let f(t) be the solution of the initial value problem
6t dy/dt + y = t^4
with f(0) = 0.
Find f(t).
f(t) = t^(4/17)

C. Find a constant c so that
k(t) = f(t) + cg(t)
solves the differential equation in part B and k(1) = 4.
c = 6

A. Let g(t) be the solution of the initial value problem
6t dy/dt + y = 0, t > 0,
with g(1) = 1.
Find g(t).
g(t) = t^(-1/6)

B. Let f(t) be the solution of the initial value problem
6t dy/dt + y = t^4
with f(0) = 0.
Find f(t).
f(t) = t^(4/17)

C. Find a constant c so that
k(t) = f(t) + cg(t)
solves the differential equation in part B and k(1) = 4.
c = 6

Added by Rachel C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

07/21/2023

Step 1

The given differential equation is: $$\frac{dy}{dt} + \frac{y}{6t} = 0$$ This is a first-order linear differential equation. We can solve it using an integrating factor. The integrating factor is given by: $$\mu(t) = e^{\int \frac{1}{6t} dt} = e^{\frac{1}{6} Show more…

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A. Let g(t) be the solution of the initial value problem 6t dy/dt + y = 0, t > 0, with g(1) = 1. Find g(t). g(t) = t^(-1/6) B. Let f(t) be the solution of the initial value problem 6t dy/dt + y = t^4 with f(0) = 0. Find f(t). f(t) = t^(4/25) C. Find a constant c so that k(t) = f(t) + cg(t) solves the differential equation in part B and k(1) = 4.