(x^(2)+y^(2))/(xy)-(x^(2))/(y(x+y))-(y^(2))/(x(x+y))
Answers
Answer:
Step-by-step explanation:
Given , Differential Equation is
(x
2
−yx
2
)dy+(y
2
+xy
2
)dx=0
This can be Simplified as
(yx
2
−x
2
)dy=(y
2
+xy
2
)dx
x
2
(y−1)dy=y
2
(1+x)dx
y
2
dy(y−1)
=
x
2
dx(1+x)
Now On Integrating both side , we get
∫
y
2
dy(y−1)
=∫
x
2
dx(1+x)
∫[
y
1
−
y
2
1
]dy=∫[
x
1
+
x
2
1
]dx
∫[
y
dy
−
y
2
dy
]=∫[
x
dx
+
x
2
dx
]
ln∣y∣−
y
1
=ln∣x∣−
x
1
+lnC
ln∣y∣−ln∣x∣−lnC=
y
1
−
x
1
ln[
c∣x∣
∣y∣
]=
xy
x−y
Video ExplanatGiven , Differential Equation is
(x
2
−yx
2
)dy+(y
2
+xy
2
)dx=0
This can be Simplified as
(yx
2
−x
2
)dy=(y
2
+xy
2
)dx
x
2
(y−1)dy=y
2
(1+x)dx
y
2
dy(y−1)
=
x
2
dx(1+x)
Now On Integrating both side , we get
∫
y
2
dy(y−1)
=∫
x
2
dx(1+x)
∫[
y
1
−
y
2
1
]dy=∫[
x
1
+
x
2
1
]dx
∫[
y
dy
−
y
2
dy
]=∫[
x
dx
+
x
2
dx
]
ln∣y∣−
y
1
=ln∣x∣−
x
1
+lnC
ln∣y∣−ln∣x∣−lnC=
y
1
−
x
1
ln[
c∣x∣
∣y∣
]=
xy
x−y