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Mathematics
Problem
Let
y
=
y
1
(
x
)
y = y_1(x)
y
=
y
1
(
x
)
and
y
=
y
2
(
x
)
y = y_2(x)
y
=
y
2
(
x
)
be two distinct solutions of the differential equation
d
y
d
x
=
x
+
y
\frac{dy}{dx} = x + y
d
x
d
y
=
x
+
y
, with
y
1
(
0
)
=
0
y_1(0) = 0
y
1
(
0
)
=
0
and
y
2
(
0
)
=
1
y_2(0) = 1
y
2
(
0
)
=
1
respectively. Then, the number of points of intersection of
y
=
y
1
(
x
)
y = y_1(x)
y
=
y
1
(
x
)
and
y
=
y
2
(
x
)
y = y_2(x)
y
=
y
2
(
x
)
is : (1) 0 (2) 1 (3) 2 (4) 3
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