I am trying to understand what "Equating the Coefficients " means
I am given the following:
$$ t_1 \left(t_2+\frac{1}{x+1}\right)+\frac{2 t_2}{x}=t_1^2 b_2'+t_1 \left(2 b_2 t_1'+b_1'\right)+b_1 t_1'+b_0'+\frac{d R}{d x}$$
and the author continues...
"Equating coefficients by $t_1$, we get the following system of equations"
$$ \begin{eqnarray} b_2' & = & 0 \\ 2 b_2 t_1'+b_1' & = & t_2+\frac{1}{x+1}\\ b_1 t_1'+b_0'+\frac{d R}{d x} & = & \frac{2 t_2}{x} \end{eqnarray} $$
"From the first equation, we find"
$$b_2=c_2$$
"From the second equation, we find"
$$\begin{array}{cc} b_1+2 c_2 t_1 & =\int (t_2+\frac{1}{x+1}) \\ \end{array}$$
I am unclear how they are arriving at this result. Help would be appreciated.
$\endgroup$ 41 Answer
$\begingroup$Basically, it means equating coefficients of each linearly independent variable from LHS and RHS. So that the identity 0=0 remains true for any value of the variables.
Here the linearly independent variables are $t_1$ and $t_1^2$ .
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