find the equation of the curve passing through (0,pi/4) whose differential equation is
sinx cosy dx + cosx siny dy =0
here cosy with dx and cosx with dy should be removed.
So divide each term with cosy cosx
the resulting equation is of variable separable type.
integrate term by term
Now to get the value of C, use the given condition that the curve passes through (0,pi/4)
put x =0 and y = pi/4 and solve for C.
Variable separable differential equation
* show that the general solution of y' + {[ (y^2)+y + 1]/[x^2+x+1] = 0is given by x+y+1=A[1-x-y-2xy]
solution of differential equation which is not homogeneous but which can be solved using x=vy
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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