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TAM3B - Differential equations
  ( x - y ) dx -( x  + y ) dy  =0 Exact Equation If the first order partial derivatives of M( x,y ) and N( x,y ) are continuous then M dx  + N dy  = 0 is an exact equation if and only if  ∂ M/ ∂ y = ∂ N/∂ x Hence to solve the exact equation  M dx  + N dy  = 0   Integrate M  with respect to x  keeping y constant Integrate those terms in N  not containing  x  with respect to   y The sum of those two integrals equated to c  is the solution. EXAMPLE 1 ( x^2-2xy+3y^2 )dx+(y^2+6xy-x^2 )dy=0 EXAMPLE 2 ( 2xy-sec^2x )dx+(x^2+2y)dy=0 EXAMPLE 3 Find the value of ‘ n ’ for which  ( x+ye^2xy )dx+nxe^2xy  dy=0    and solve it   EXAMPLE 4 ( sin x. tan y+1)dx-(cosx.sec^2y )dy=0 EXAMPLE 5 ( e^y+1)  cos x  dx+e^y  sinx  dy=0


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