Question

solve the differential equation dy/dx=x+y+1/2x+2y+3​

Answer 1

Answer:

ANSWER

dx

dy

=

2x+2y+3

x+y+1

Put x+y=v

1+

dx

dy

=

dx

dv

⇒

dx

dv

−1=

2v+3

v+1

⇒

dx

dv

=

2v+3

3v+4

⇒

3v+4

(2v+3)dv

=dx

Integrating both sides,

∫

3v+4

(2v+3)dv

=∫dx

⇒

3

1

∫

3v+4

2(3v+4)dv

+

3

1

∫

3v+4

1dv

=x+logc

⇒

3

2

v+

9

1

log3v+4=x+logc

⇒

9

1

log(3x+3y+4)−logc=

3

1

(x−2y)

⇒log

c

(x+y+

3

4

)

=3(x−2y)

x+y+

3

4

=ce

3(x−2y)

Comparing with given solution, we get

k=4