Question

Find the general solution, y(t), which solves the problem below, by the method of integrating factors.

Answer 1

The general solution, y(t), which solves the problem by the method of integrating factors is; y = ¹/₂₁t⁴ + (1/t)c₁t^(⁴/₅)

How to solve differential equations?

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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