Help with Integration Step in y'=1+0.01y^2 Problem - Expert Advice

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The discussion centers on the integration step for the differential equation y' = 1 + 0.01y^2. The user correctly rewrites the equation as dy/(1 + 0.01y^2) = dx but encounters difficulty with the integration. They express that the integral resembles an arctangent function, indicating a potential solution. Other participants remind them of the arctan function's relevance in this context, emphasizing its importance in solving the problem. The conversation highlights the need to recall specific integration techniques when tackling such equations.
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In the problem, y`= 1+0.01y^2
the first i took was
dy/(1+0.01y^2)=dx
however, I'm stuck on the integration step...
can someone help?
 
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\int {\frac{{dy}}{{1 + 0.01y^2 }}} = \int {\frac{{dy}}{{1 + \left( {\frac{y}{{10}}} \right)^2 }}} = 10\int {\frac{{d\left( {\frac{y}{{10}}} \right)}}{{1 + \left( {\frac{y}{{10}}} \right)^2 }}}

The last one smells arctan-ish :smile:
 
jeepers! thanks for reminding me about the arctan-ish thingy...
crud, totally forgot about that one~
:)
 
No problem; but never forget the arctan hehe :biggrin:
 

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