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]
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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