1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Linear Differential Equations of First Order
The solution ...
Question
The solution of
y
d
x
−
x
d
y
+
log
x
d
x
=
0
is:
A
y
−
log
x
−
1
=
c
x
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
x
+
log
x
+
1
=
c
x
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
y
+
log
x
+
1
=
c
x
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
y
+
log
x
−
1
=
c
x
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is
A
y
−
log
x
−
1
=
c
x
Given,
y
d
x
−
x
d
y
+
log
x
d
x
=
0
⇒
y
−
x
d
y
d
x
+
log
x
=
0
⇒
y
−
log
x
=
x
d
y
d
x
⇒
y
x
−
log
x
x
=
d
y
d
x
⇒
d
y
d
x
+
(
−
1
x
)
y
=
−
log
x
x
Here, the above equation is a linear differential equation of the form,
d
y
d
x
+
P
(
x
)
y
=
Q
(
x
)
where,
P
(
x
)
=
−
1
x
and
Q
(
x
)
=
−
log
x
x
Thus, Integrating factor
=
e
∫
P
(
x
)
d
x
=
e
∫
−
1
x
d
x
=
e
−
log
x
=
x
−
1
Hence, the general solution is
y
×
I
.
F
.
=
∫
Q
(
x
)
×
I
.
F
.
d
x
⇒
y
×
(
x
−
1
)
=
∫
(
−
log
x
x
)
×
x
−
1
d
x
⇒
y
x
=
−
∫
log
x
x
2
d
x
=
−
[
(
log
x
)
(
−
1
x
)
−
∫
1
x
×
−
1
x
d
x
]
⇒
y
x
=
log
x
x
+
1
x
+
c
⇒
y
=
log
x
+
1
+
c
x
⇒
y
−
log
x
−
1
=
c
x
Suggest Corrections
0
Similar questions
Q.
If
y
=
√
log
x
+
√
log
x
+
√
log
x
+
.
.
.
.
.
.
∞
then
d
y
d
x
=
1
x
(
2
y
−
1
)
Q.
y
=
√
l
o
g
x
+
√
l
o
g
x
+
√
l
o
g
x
+
_____
∞
show that
d
y
d
x
=
1
x
(
2
y
−
1
)
.
Q.
If
y
=
√
log
x
+
√
log
x
+
√
log
x
+
.
.
.
∞
show that
d
y
d
x
=
1
x
(
2
y
−
1
)
.
Q.
If
y
=
√
log
x
+
2
√
log
x
+
2
√
log
x
+
⋯
∞
, then
d
y
d
x
at
x
=
1
is
Q.
The solution of the differential equation
x
d
y
d
x
=
y
1
+
log
x
is :
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Methods of Solving First Order, First Degree Differential Equations
MATHEMATICS
Watch in App
Explore more
Linear Differential Equations of First Order
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app