• Let the differential equation be :
• Common part=
• g(y)= =>
If we try to find the general solution of
if we do
but the above integrations doesn't
have commonpart or h(x) and g(y).
To find G.S for the above equation we
reduce it to exact equation.
let us know what is exact equation..
Let's know what is exact equation ?
• Remember , order doesn't matter for partial derivatives:
To solve the differential of the form M(x,y)+N(x,y)y'=0 the necessary
• => and the above equation is called exact.
To solve problems of the form
Step 1:- Observe
Step 2:-Compute Mdx + Ndy
Step 3:- write the general solution as
f(x,y)= M(x,y)dx+ N(x,y)dy
If a differential equation Mdx+Ndy=0
which is not exact can be made
exact by multiplying it with a
suitable µ(x,y)≠0 then µ(x,y) is called
an integrating factor of the equation