auto ad

Tuesday, January 31, 2017

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 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

disclaimer:
There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work




No comments:

Post a Comment

please leave your comments