The general solution, y(t), which solves the problem by the method of integrating factors is; y = ¹/₂₁t⁴ + (1/t)c₁t^(⁴/₅)
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; https://brainly.com/question/17201048
#SPJ1
