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Question Number 97137 by mhmd last updated on 06/Jun/20

u s i n g a p a r t i c u l a r t h e o r y, f i n d t h e g e n e r a l s o l u t i o n t o

t h e f o l l o w i n g d i f f e r e n t i a l e q u a t i o n

f (x + y) d x + g (x + y) d y = 0 ?

h e l p m e s i r p l e a s e

Commented by prakash jain last updated on 06/Jun/20

what do u mean by a particular

theory ?

Commented by mhmd last updated on 07/Jun/20

S p e c i f i c t h e o r e m s i r

Answered by mr W last updated on 07/Jun/20

\frac{d y}{d x} = - \frac{f (x + y)}{g (x + y)}

l e t u = x + y

\frac{d y}{d x} = \frac{d u}{d x} - 1

\frac{d u}{d x} - 1 = - \frac{f (u)}{g (u)}

\frac{g (u) d u}{g (u) - f (u)} = d x

\Rightarrow x = \int \frac{g (u) d u}{g (u) - f (u)} = h (u) + C

\Rightarrow x = h (x + y) + C

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