2ydx+3xdy=xy3dy;x=1 y=1

Vikolers6

Vikolers6

Answered

2021-12-19

2ydx+3xdy=xy3dy;x=1 y=1

Answer & Explanation

Marcus Herman

Marcus Herman

Expert

2021-12-20Added 41 answers

Step 1
we have to solve the given differential equations with intial condition.
We can solve it variable seperable
Step 2
Given 2ydx+3xdy=xy3dy;x=1 y=1
2ydx=xy3dy3xdy
2ydx=x(y33)dy
2dxx=(y33y)dy
2dxx=(y23y)dy
2ln(x)=y333ln(y)+c (1)
Put x=1,y=1
2ln(1)=1333ln(1)+c
0=10+c
c=1
Put c=1  (1)
2ln(x)=y333ln(y)1
(1) dxx=ln(x)+c (2) xndx=xn+1n+1+c
amarantha41

amarantha41

Expert

2021-12-21Added 38 answers

We need to solve 2ydx+3xdy=xy3dy,y(1)=1
So, 2ydx+3xdy=xy3dy
2y+3xdydx=xy3dydx
Substitute dydx with y
RizerMix

RizerMix

Expert

2021-12-29Added 437 answers

2ydx=(xy33x)dy
2ydx=x(y33)dy
Now using sepration of variable method then
2dxx=(y33)ydy
Integrating both side then
2dxx=(y23y)dy
2lnx=y333lny+c (1)
Now, given initial condition x=1, y=1
Now by Eqn (1)
2ln(1)=133ln1+c
2×0=130+c
c=13
Put value of c in eq-n (1) then
2lnx=y333lny13
y333lny=2lnx+13

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