Differential Equations Worksheets With Answers - Ncert/cbse Mathematics Class 12 Page 3
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4NCERT/CBSE MATHEMATICS CLASS 12 textbook
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29( )
iii
y
=
x
sin 3
x
dy
d
dx
⇒
=
x
sin 3
x
+
sin 3
x
dx
dx
dx
dy
⇒
=
3 cos 3
x
x
+
sin 3 .1
x
dx
2
d y
d
dx
d
⇒
=
3[
x
cos 3
x
+
cos 3
x
]
+
sin 3
x
2
dx
dx
dx
dx
2
d y
⇒
=
3[ ( sin 3 ) cos 3 .1] 3cos 3
x
−
x
+
x
+
x
2
dx
2
d y
⇒
= −
9 sin 3
x
x
+
3cos 3
x
+
3cos 3
x
2
dx
2
d y
⇒
+
9
y
−
6 cos 3
x
= −
9 sin 3
x
x
+
3cos 3
x
+ cos 3
3
x
+
9 sin 3
x
x
+
6 cos 3
x
=
0
2
dx
The given expression is not a solution of the given differential equation
2( )
iv
2
2
x
=
2
y
log
y
2
d
d
dy
2
2
x
=
2 log
y
y
+
2 log
x
dx
dx
dx
1
dy
dy
⇒
2
2
x
=
2
y
+
2 log (2 )
y y
y dx
dx
dy
⇒ = +
x
y
log (2 )
y y
dx
dy
⇒ =
[
]
x
y
+
2 log
y
y
dx
dy
⇒
2
2
xy
=
y
+
2
y
log
y
dx
2
2
But x
,
=
2
y
log
y
dy
⇒
2
2
xy
y
x
=
+
dx
dy
⇒
2
2
y
+
x
−
xy
=
0
dx
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