-->

Differential Equations

Question
CBSEENMA12033147

Find a particular solution of the differential equation
(x – y) (dx + dy) = dx – dy. given that y = – 1, when x = 0.

Solution
The given differential equation is
              (x – y) (dx + dy) = dx – dy                          ...(1)
or             dx plus dy space equals space fraction numerator dx minus dy over denominator straight x minus straight y end fraction
Integrating, we get
                      integral left parenthesis dx plus dy right parenthesis space equals space integral fraction numerator straight d space left parenthesis straight x minus straight y right parenthesis over denominator straight x minus straight y end fraction plus straight c
rightwards double arrow space space space space space space space space space space space space straight x plus straight y space equals space log space open vertical bar straight x minus straight y close vertical bar plus straight c                        ....(2)
Now x = 0,  y = -1
therefore space space space space space space space 0 plus left parenthesis negative 1 right parenthesis space equals space log space open vertical bar 0 plus 1 close vertical bar space plus space straight c
rightwards double arrow space space space space space space space space space space space straight c space equals space minus 1
therefore space space space from space left parenthesis 2 right parenthesis comma space space space straight x plus straight y space equals space log space open vertical bar straight x minus straight y close vertical bar space minus space 1
which is required solution.

Some More Questions From Differential Equations Chapter