find a particular solution of the differential equation [dy/dx]+ycotx =4xcosecx [x is not 0] given that y =0 if x=pi/2
the equation is an example of linear differential equation, so compare [dy/dx]+ycotx =4xcosecx with the standard linear differential equation [dy/dx]+Pycotx =Q
Identify the values of P and Q
here P=cotx
Q=4xcosecx
Find the integrating factor[I.F.] = e^[integral of P ]
use the result e^[ln{f(x)}] = f(x)
use the solution
y[I.F.] = integral of [ Q* I.F. ] +C
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is given by x+y+1=A[1-x-y-2xy]
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formulae on integration
PAGE 1 BASIC INTEGRATION
PAGE 2 INTEGRATION BY SUBSTITUTION
PAGE 3 INTEGRATION BY COMPLETION OF SQUARES
PAGE 4 INTEGRATION BY PARTS
PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR
PAGE 6 INTEGRATION USING PARTIAL FRACTIONS
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