solve (1+x2)dy/dx-x=2tan-1x
Answers
Answered by
0
Answer:
check my brain list and free point me
Answered by
0
Answer:
ANSWER
(1+x
2
)
dx
dy
−x=2tan
−1
x
⇒(1+x
2
)
dx
dy
=x+2tan
−1
x
⇒dy=(
1+x
2
x+2tan
−1
x
)dx
Integrating both sides, we have
∫dy=∫(
1+x
2
x+2tan
−1
x
)dx
y=∫
1+x
2
x
dx+∫
1+x
2
2tan
−1
x
dx
⇒y=
2
1
log
∣
∣
∣
1+x
2
∣
∣
∣
+∫
1+x
2
2tan
−1
x
dx.....(1)
Now,
∫
1+x
2
2tan
−1
x
dx
Let tan
−1
x=t
1+x
2
1
dx=dt
∫2tdt=2⋅
2
t
2
+C=t
2
+C=(tan
−1
x)
2
+C
⇒∫
1+x
2
2tan
−1
x
dx=(tan
−1
x)
2
+C.....(2)
From equation (1) and (2), we have
y=
2
1
log
∣
∣
∣
1+x
2
∣
∣
∣
+(tan
−1
x)
2
+C
Hence the solution for the given differential equation is y=
2
1
log
∣
∣
∣
1+x
2
∣
∣
∣
+(tan
−1
x)
2
+C.
Similar questions