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Tuesday, January 31, 2017

linear differential equation for cbse ncert miscellaneous problem

linear differential equation for cbse ncert miscellaneous problem

solve [ { e^[-2sqrt(x)] / sqrt(x) } - {y / sqrt(x)}] [dx/dy] = 1  [x is not 0]

here there is only one term in y

so we have to rearrange the equation in the form

[dy/dx] + Py = Q

identify the values of P and Q

find the integrating factor e^[integral of P]

and use in the solution

y[integrating factor] = integral of [Q*integrating factor] + C









Variable separable differential equation
*find the equation of the curve passing through (0,pi/4) whose differential equation is
sinx cosy dx +  cosx siny dy =0
solution of  variable separable differential equation find the equation of the curve passing through (0,pi/4) whose differential equation issinx cosy dx +  cosx siny dy =0

* 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]

*solve y e^(x/y) = [ y e^(x/y) + (y^2) ]dy  [ y is not equal to 0]
solution of differential equation which is not homogeneous but which can be solved using x=vy



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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