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Byju's Answer
Standard VIII
Mathematics
ASA Postulate
the solution ...
Question
the solution of x∫_0^xy(t)dt=(x+1)∫_0^xt.y(t)dt,x>0,i
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Similar questions
Q.
Let
a
>
0
,
a
≠
1
and
x
>
0
(i)
log
a
x
>
0
,
a
>
1
⇔
x
>
0
,
a
>
1
(ii)
log
a
x
>
0
,
0
<
a
<
1
⇔
0
<
x
<
1
,
0
<
a
<
1
(iii)
log
a
x
>
0
,
a
>
1
⇔
0
<
x
<
1
,
a
>
1
(iv)
log
a
x
<
0
,
0
<
a
<
1
⇔
x
>
1
,
0
<
a
<
1
What is the solution set of
log
3
5
−
2
x
12
x
−
8
+
log
1
/
3
x
≤
0
?
Q.
Based on this information answer the given queston:
Let
a
>
0
,
a
≠
1
and
x
>
0
(i)
log
a
x
>
0
,
a
>
1
⇔
x
>
0
,
a
>
1
(ii)
log
a
x
>
0
,
0
<
a
<
1
⇔
0
<
x
<
1
,
0
<
a
<
1
(iii)
log
a
x
>
0
,
a
>
1
⇔
0
<
x
<
1
,
a
>
1
(iv)
log
a
x
<
0
,
0
<
a
<
1
⇔
x
>
1
,
0
<
a
<
1
Identify the solution set of
x
if
log
1
/
10
(
x
2
+
x
+
1
)
>
0
Q.
Find the general solution of each equation:
(
i
)
√
3
c
o
t
x
+
1
=
0
(
i
i
)
c
o
s
e
c
x
+
√
2
=
0
Q.
For each of the following differential equations, find a particular solution satisfying the given condition:
(i)
x
x
2
-
1
d
y
d
x
=
1
,
y
=
0
when
x
=
2
(ii)
cos
d
y
d
x
=
a
,
y
=
1
when
x
=
0
(iii)
d
y
d
x
=
y
tan
x
,
y
=
1
when
x
=
0
Q.
Find a particular solution of each of the following differential equations:
(i)
1
+
x
2
d
y
d
x
+
2
x
y
=
1
1
+
x
2
;
y
=
0
,
when
x
=
1
(ii) (x + y) dy + (x − y) dx = 0; y = 1 when x = 1
(iii) x
2
dy + (xy + y
2
) dx = 0; y = 1 when x = 1
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