Solve for G.S. / P.S. for the following differential equations using separation of variables. x^2ydy-xy^2dx+3ydy-2xdx=0

pancha3

pancha3

Answered question

2021-09-04

Solve for G.S. / P.S. for the following differential equations using separation of variables.
x2ydyxy2dx+3ydy2xdx=0

Answer & Explanation

falhiblesw

falhiblesw

Skilled2021-09-05Added 97 answers

Step 1
Given data:
The given differential equation is x2ydyxy2dx+3ydy2xdx=0
The given expression can be written as,
(x2y+3y)dy=(xy2+2x)dx
(x2+3)ydy=(y2+2)xdx
yy2+2dy=xx2+3dx
12(2yy2+2)dy=12(2xx2+3)dx
Integrate the above expression.
12(2yy2+2)dy=12(2xx2+3)dx
Step 2
Assume y2+2=t,x2+3=u and differentiate both the equation with respect to y and x respectively.
ddy(y2+2)=dtdy
dy=dt2y(I)
ddx(x2+3)=dudx
dx=du2x(II)
Substitute the above equations in the integral.
12(2yt)(dt2y)=12(2xu)(du2x)

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