(x^2y-2xy^2)dx-(x^3-3x^3y)dy=0
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Solve:
(x
2
y−2xy
2
)dx=(x
3
−3x
2
y)dy.
Medium
Solution
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(x
2
y−2xy
2
)dx=(x
3
−3x
2
y)dy
(x
2
y−2xy
2
)dx−(x
3
−3x
2
y)dy=0
Here,
M=x
2
y−2xy
2
⇒
∂y
∂M
=x
2
−4xy
N=−(x
3
−3x
2
y)⇒
∂x
∂N
=6xy−3x
2
∵
∂y
∂M
=
∂x
∂N
Therefore,
Integrating factor =
Mx+Ny
1
=
x(x
2
y−2xy
2
)+y(3x
2
y−x
3
)
1
=
x
2
y
2
1
Step-by-step explanation:
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