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Sunday, February 5, 2017

linear differential equation y dx + [x-(y^2)]dy = 0

linear differential equation from ncert cbse

solve y dx + [x-(y^2)]dy = 0

The equation contains only one x term

Therefore try to solve for [dx/dy] and compare with the linear differential equation of the form

[dx/dy] + Px = Q

Then compare and get the values of P and Q

find the integrating factor of the linear differential equation using the formula

I.F. = e^[integral of P dx]

use the property e^[ln[f(y)] = f(y)

then use the solution

x[I.F.] = integral of [ Q * I.F.]dy +C



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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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