How Do You Solve the Differential Equation dx/dt = cos(x + t)?

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Homework Help Overview

The discussion revolves around solving the differential equation dx/dt = cos(x + t), which falls under the subject area of differential equations.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts a substitution method involving z = sin(x) but notes that it quickly fails. Another participant suggests a simpler approach, hinting that expanding cos(x + t) may not be necessary. A different approach using the substitution z = x + t is also mentioned, leading to a separation of variables.

Discussion Status

The discussion is ongoing, with participants exploring different methods and providing hints. There is no explicit consensus, but some guidance has been offered regarding the potential simplification of the problem.

Contextual Notes

Participants are navigating various substitution methods and questioning the necessity of certain expansions in their approaches. The original poster's attempt indicates a struggle with the initial substitution, while others are exploring alternative strategies.

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Homework Statement



solve the differential eqn: dx/dt=cos(x+t)

Homework Equations





The Attempt at a Solution



x'=cos(x+t)=cosxcost-sinxsint

let z=sinx, dz/dx=cosx

dz/dt=(dz/dx).(dx/dt)=cosx(dx/dt)

however this substitution quickly fails

any ideas?

thanksx
 
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Try something simpler. Hint: You don't need to expand cos(x+t).
 
Used z=x+t

get: int(1/(cosz+1)=in(t) on separation of the variables.

cheers
 
Can you finish the problem now?
 

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