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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