Solve differential equationdy/dx+xy=xy^2

coexpennan

coexpennan

Answered question

2021-01-13

Solve differential equation dydx+xy=xy2

Answer & Explanation

ottcomn

ottcomn

Skilled2021-01-14Added 97 answers

dydx+xy=xy2
dydx=xy2xy
dydx=xy(y1)
dyy(y1)=xdx
1y(y1)=Ay+By1
1=A(y1)+By
1=(A+B)yA
Comparing the coefficient of y and constant term on both side, we get
A+B=0, A=1A=1, B=1
So, we write
1y(y1)=1y+1(y1)
So, we have
(1y+1(y1))dy=xdx
Now, we will integrate this equation on both the side
(1y+1(y1))dy=xdx ln(y)+ln(y1)=x22+C
y1y=x22+C
y1y=ex22+C
y1y=ex22eC
y1y=C1ex22, C1=eC
where C and C1 are arbitrary constant
y1=C1ex22y
y=C1ex22y+1
yCex22y=1
y(1C1ex22)=1
y=11C1ex22

Jeffrey Jordon

Jeffrey Jordon

Expert2021-10-22Added 2605 answers

Answer is given below (on video)

Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-14Added 2605 answers

Answer is given below (on video)

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