variable separable differential equation for cbse ncert 12th

variable separable differential equation for cbse ncert 12th

show that the general solution of y' + {[ (y^2)+y + 1]/[x^2+x+1] = 0
is given by x+y+1=A[1-x-y-2xy]

first separate the variables , then, complete the squares in each term,  integrate term by term
then use the formula for arctanx+arctany

 

homogeneous differential equation
prove that [ x^2 - y^2 ]=c [ x^2 - y^2 ]^2 is a solution of
[ x^3 - 3x (y^2) ] dx = [ y^3 - 3x^2y ] dy

solution of homogeneous differential equation from miscellaneous problems of ncert cbse 12th mathematics

solution of a second order differential equation using reduction of order
solve y"-y = 0 if y = coshx is one of the solutions
using the formula for reduction of order
solution of solution of a second order differential equation using reduction of order

variation of parameter method

solve xy" - 4y' = x^4 by method of variation of parameter
solution to problem on differential questions using variation of parameter method

orthogonal trajectory of y(1+x ² ) = Cx

find the orthogonal trajectory of y(1+x ² ) = Cx
answer to problem on  orthogonal trajectory of y(1+x ² ) = Cx

orthogonal trajectory of y = (k/x)

find the orthogonal trajectory of y = (k/x)
solution to  find the orthogonal trajectory of y = (k/x)



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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