Question

Solve:(5x+6y)dx+(8y^3-6x)dy=0

Answer 1

→dy/dx=5x+6y/6x-8y^3 →(1)

Answer 2

x→1/t:y(x)→y(t) ,

Answer 3

dy?dx=dy/dt(dt/dx)

Answer 4

= -t^2 dy/dt →(2)

Answer 5

(1),(2)→ -t^2•dy/dt

Answer 6

(5/t)+6y/(6/t)-8y^3

Answer 7

→ dy/dt=5+6yt/8ty^5-6t^2 ,

Answer 8

(5+6yt)dt+(6t^2-8ty^5)dy=0

Answer 9

P_=5+6yt

Answer 10

Q_=t•(6t-8y^5)

Answer 11

æp/æy=6t

Answer 12

æQ/æt=12t-8y^5

Answer 13

{6t-(12t-8y^5)/t(6t-8y^5) dt

Answer 14

={-dt/t

Answer 15

If=1/t , If≠1

Answer 16

→Ē u(y,t):

Answer 17

du_= u,t dt+ u ,y dy=0

Answer 18

U=CONST.

Answer 19

æu/æy_=IfQ

Answer 20

= 6t-8y^5

Answer 21

→ u_=6ty-40y^4+w(t)→(3)

Answer 22

æu/æt=6y+w'(t)_= IfP

Answer 23

→w‘(t)= 5/t

Answer 24

W(t)= lnt^5 →(4)

Answer 25

(3),(4)→ u_= 6ty-40y^4+5 lnt=c →(5)

Answer 26

t→ 1/x : 6y/x-40y^4-5 lnx=c →(6)