non homogeneous equation with the substitution x=vy

miscellaneous problem from ncert differential equation where the substitution x=vy still works even though is not a homogeneous equation

solve y e^(x/y) = [ y e^(x/y) + (y^2) ]dy  [ y is not equal to 0]

here there  are terms containing [x/y]
so extract dx/dy call the value of dx/dy as f[x,y]
replace x with tx and y with ty and check if the function is homogeneous

here f[tx,ty] is not equal to f[x,y]
therefore the function is not homogeneous

but the substitution v =(x/y) will still work for this problem

Variable separable differential equation

* 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 variable separable differential equation from ncert cbse miscellaneous problem

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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