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

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

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]

solution of differential equation which is not homogeneous but which can be solved using x=vy

*linear differential equation

solve [ { e^[-2sqrt(x)] / sqrt(x) } - {y / sqrt(x)}] [dx/dy] = 1 [x is not 0]solution of linear differential equation of ncert cbse miscellaneous differential equation

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 parametersolution 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 ) = Cxanswer 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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