Solving ODE dy/dx = (x+y)^2 , y(0)=1

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Homework Help Overview

The discussion revolves around solving the ordinary differential equation (ODE) dy/dx = (x+y)^2 with the initial condition y(0)=1. Participants are exploring the transformation of the equation and the implications of their substitutions.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the substitution w = (x+y) and its impact on the equation, leading to a rearrangement and exploration of the resulting differential equation. There are attempts to verify the correctness of the initial conditions and the transformations applied.

Discussion Status

The discussion is ongoing, with participants checking their transformations and initial conditions. Some have provided insights into the relationships between the variables and their derivatives, while others are seeking confirmation of their reasoning.

Contextual Notes

There is a focus on verifying initial conditions and ensuring that the transformations align with the original problem statement. Participants are navigating through the implications of their substitutions and the correctness of their derived expressions.

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solve dy/dx = (x+y)^2 , y(0)=1

i let w = (x+y) and got the above equation rearranged to dw/dx - 1=w^2

after solving for C i got y=tan(x-pi/4) - x

just wanted to check my answer
 
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w = (x+y) then
dw/dx = 1+dy/dx
dw/dx = 1 + w^2

this part looks ok
 


then
w = x+y=x+(tan(x-pi/4)-x) = tan(x-pi/4)
dw/dx = sec(x-pi/4)^2 = 1+tan(x-pi/4)^2
 


just remains to check IC
w(0) = tan(-pi/4)

does that look correct?
 

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