(i)
2
2
2
5
6
log
d y
xdy
y
x
dx
dx
⎛
⎞
+
−
=
⎜
⎟
⎝
⎠
         (ii)  
3
2
4
7
sin
dy
dy
y
x
dx
dx
⎛
⎞
⎛
⎞
−
+
=
⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠
(iii)
4
3
4
3
sin
0
d y
d y
dx
dx
⎛
⎞
−
=
⎜
⎟
⎝
⎠
© NCERT
not to be republished
MATHEMATICS
420
2 For each of the exercises given below, verify that the given function (implicit or
explicit) is a solution of the corresponding differential equation (i) y = a ex + b e–x + x2
:
2
2
2
2
2
0
d y
dy
x
xy
x
dx
dx
+
−
+
−
=
(ii) y = ex (a cos x + b sin x)
:
2
2
2
2
0
d y
dy
y
dx
dx
−
+
=
(iii) y = x sin 3x
:
2
2
9
6cos3
0
d y
y
x
dx
+
−
=
(iv) x2 = 2y2 log y
:
2
2
(
)
0
dy
x
y
xy
dx
+
−
=
3 Form the differential equation representing the family of curves given by
(x – a)2 + 2y2 = a2, where a is an arbitrary constant