Help to solve the following first order differential equations: a. xy^4dx+(y^2+2)e^{-5x}dy=0 b.(x+1)y'=x+6

Krzychau1

Krzychau1

Answered question

2022-01-21

Help to solve the following first order differential equations:
a. xy4dx+(y2+2)e5xdy=0
b.(x+1)y=x+6

Answer & Explanation

macalpinee3

macalpinee3

Beginner2022-01-21Added 29 answers

a. Solution:
xy4dx+(y2+2)e5xdy=0
  xy4dx=(y2+2)e5xdy
xe5xdx=(y2+2y4)dy
(1y22y4)dy=xe5xdx
1y2dy21y4dy=xe5xdx+c
[y2+12+1]2[y4+14+1]=xe5x515e5xdx+c
1y+23y3=xe5x5125e5x+c
(y2+23)=(x5125)y3e5x+y3c
psor32

psor32

Beginner2022-01-22Added 33 answers

b. (x+1)y=x+6
(x+1)dydx=(x+6)
dy=(x+6x+1)dx
dy=(x+1)+5(x+1)dx
dy=(1+5x+1)dx
dy=(1+5x+1)dx+c
y=x+5log(x+1)+c

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