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1. Show that y=2*e^(5x)+4x is a solution to the differential equation y'-5y=4-20x2. Determine eventual max, min and saddle points in the function f(x)=x^3-6x^2-15x+243. Determine the biggest and...

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1. Show that y=2*e^(5x)+4x is a solution to the differential equation y'-5y=4-20x2. Determine eventual max, min and saddle points in the function f(x)=x^3-6x^2-15x+243. Determine the biggest and smallest value of teh function y=cos(x)+x*sin(x) in the interval 0=x=2*pi. An exact answer is needed.
Answered Same Day Dec 22, 2021

Solution

Robert answered on Dec 22 2021
121 Votes
1. Show that y=2*e^(5x)+4x is a solution to the differential equation y'-5y=4-20x


This is linear differential Equation question.
Integrating Factor (IF) = ∫
Hence solution is
∫
∫
∫ ∫
Using integration by parts -



[

∫


]



[


]





Where C is integration...
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