Solve the following first order differential equations: 1. (1+x^2+y^2+x^2y^2)dy=y^2dx 2. e^xy\frac{dy}{dx}=e^{-y}+e^{3x-y}

Madeline Lott

Madeline Lott

Answered question

2022-01-20

Solve the following first order differential equations:
1. (1+x2+y2+x2y2)dy=y2dx
2. exydydx=ey+e3xy

Answer & Explanation

yotaniwc

yotaniwc

Beginner2022-01-20Added 34 answers

1. (1+x2+y2+x2y2)dy=y2dx
((1+x2)+y2(1+x2))dy=y2dx
(1+x2)(1+y2)dy=y2dx
(1+y2)y2dy=dx(1+x2)
1y2dy+dy=11+x2dx+c
y2+12+1+y=tan1x+c
1y+y=tan1(x)+c
(y1y)=tan1(x)+c
Esta Hurtado

Esta Hurtado

Beginner2022-01-21Added 39 answers

2. exydydx=ey+e3xy
  exydydx=ey+e3xey
exydydx=ey(1+e3x)
ydyey=(1+e3xex)dx
yeydy=(ex+e2x)dx
yeydy=(ex+e2x)dx+c
yeyey=ex+e2x2+c
2(yeyy)+2exe2x=c

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