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Test Index
JEE Main Math Class 12 Differential Equations Part 2 Questions
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Section:
Mathematics
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© examsnet.com
Question : 1
Total: 107
Let
x
=
x
(
t
)
and
y
=
y
(
t
)
be solutions of the differential equations
dx
dt
+
ax
=
0
and
dy
dt
+
by
=
0
respectively,
a
,
b
∈
R
. Given that
x
(
0
)
=
2
;
y
(
0
)
=
1
and
3
y
(
1
)
=
2
x
(
1
)
, the value of
t
, for which
x
(
t
)
=
y
(
t
)
, is :
[27-Jan-2024 Shift 1]
log
2
3
2
log
4
3
log
3
4
log
4
3
2
Validate
Solution:
👈: Video Solution
d
x
d
t
+
a
x
=
0
d
x
x
=
−
a
dt
∫
d
x
x
=
−
a
∫
dt
ln
|
x
|
=
−
a
t
+
c
a
t
t
=
0
,
x
=
2
ln
2
=
0
+
c
ln
x
=
−
a
t
+
ln
2
x
2
=
e
−
a
t
x
=
2
e
−
a
t
..............(I)
d
y
d
t
+
b
y
=
0
d
y
y
=
−
b
dt
ln
|
y
|
=
−
b
t
+
λ
t
=
0
,
y
=
1
0
=
0
+
λ
y
=
e
−
bt
.................(II)
According to question
3
y
(
1
)
=
2
x
(
1
)
3
e
−
b
=
2
(
2
e
−
a
)
e
a
−
b
=
4
3
For
x
(
t
)
=
y
(
t
)
⇒
2
e
−
at
=
e
−
bt
2
=
e
(
a
−
b
)
t
2
=
(
4
3
)
t
log
4
3
2
=
t
© examsnet.com
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