The general solution, y(t), which solves the problem by the method of integrating factors is; y = ¹/₂₁t⁴ + (1/t)c₁t^(⁴/₅)
<h3>How to solve differential equations?</h3>
We want to find the general solution of;
5t(dy/dt) + y = t⁴
We will divide through by 5t to get;
(dy/dt) + y/5t = t³/6
Using Integration factor, we have;
u(t) = e^∫(¹/₅t) dt = t^(¹/₅)
Thus, we now have;
[t^(¹/₅)](dy/dt) + [t^(¹/₅)]y/5t = [t^(¹/₅)]t³/6
Completing this with a differential calculator gives us the general solution as;
y = ¹/₂₁t⁴ + (1/t)c₁t^(⁴/₅)
Read more about differential equations at; brainly.com/question/17201048
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Answer:
Step-by-step explanation:
communicative because you moved the three to the other side
Answer:
Explanation: Remember the standard linear equation: y=mx+b. The variables 'mx' represent the slope of a linear line meaning in the equation y=4, there is no slope, or a slope of 0.
Step-by-step explanation:
As y=4x−2 can be written as y=4x+(−2) . Hence, it's slope is 4 and intercept on y -axis is −2 .
It's been awhile since I've worked with infinite series and partial sums, but here are my thoughts:
A. the first 4 terms: -4,

,

,

B. In examining the partial sums of the series, it appears that the sequence produced has a limit and therefore the series would be convergent.
C. the limit or sum of the series looks to be -5 Below look at the sequence of partial sums:
-4,

,

,

So you can see we're getting closer and closer to -5