(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 4 Prove that x2 – y2 = c (x2 + y2)2 is the general solution of differential equation
(x3 – 3x y2) dx = (y3 – 3x2y) dy, where c is a parameter