How to integrate 13e^(-0.2x)sin(x)

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Homework Help Overview

The discussion revolves around the integration of the function 13e^(-0.2x)sin(x) and the differential equation dy/dx = x - 4 + xy - 4y, with an initial condition y(0) = 4. Participants are exploring methods for solving these problems within the context of calculus and differential equations.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to use the method of solving for the unknown integral by integrating the function multiple times. There are questions about how to manipulate the differential equation to isolate x and y. Some participants discuss the factorability of the right-hand side of the differential equation.

Discussion Status

Some participants have made progress in solving the integral, with one claiming to have found the solution. However, there are indications of uncertainty and corrections being made regarding the integration results. The discussion remains active with ongoing exploration of the differential equation.

Contextual Notes

There are indications of confusion regarding the integration process and the correct formulation of the differential equation. The original poster's attempts to clarify their approach suggest a need for further exploration of the methods involved.

killerinstinct
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what is the integral of 13e^(-0.2x) sinx?

i'm using the solving for the unknown integral method.
i did this twice (each time i took the integral twice, moved the unknown integral to the same side, and divided by 13.52?? I still cannot figure out what i am doing wrong.


solve for the diffential. dy/dx = x-4+xy-4y y(0)=4
how can i move it so that x is on one side and y on the other? what is the integral of xy?
 
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killerinstinct said:
solve for the diffential. dy/dx = x-4+xy-4y y(0)=4
how can i move it so that x is on one side and y on the other? what is the integral of xy?
The RHS is factorable into a function of x and a function of y.
 
nvm the first problem. I solved it.
the integral =

12.5e^(-.2x) sinx + 2.5e^(-.2x) cosx
 
oops, its should be a - in between.
 
oops still wrong. this is right: -12.5e^(-.2x) cosx - 2.5e^(-.2x) sinx
 
(x-4)(y+1)! Now i see it, thank you!
 

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