form the differential equation of the family of circles in the first quadrant which touch the coordinate axes
Take the radius as r so that the centre is (r,r)
write the equation of the circle in terms of r
r is the aribitrary constant.
so differentiate it one time with respect to x and use
that to solve for r
substitute into (x-r) and (y-r) and substitute into the equation of the
circle to eliminate r
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
solution to problem on differential questions using variation of parameter method
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)
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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