Let f : [0,1]
R be such that f(xy)=f(x).f(y) for all x,y,
[0,1], andf(0)
0. If y=y(x) satisfies the differential equation, 
=f(x) with y(0)=1, then y
y
is equal to
a.
4
b.
3
c.
5
d.
2
R be such that f(xy)=f(x).f(y) for all x,y, [0,1], andf(0) 0. If y=y(x) satisfies the differential equation, =f(x) with y(0)=1, then y y is equal toa.
4
b.
3
c.
5
d.
2
Question ID - 56767 | SaraNextGen Top Answer Let f : [0,1] R be such that f(xy)=f(x).f(y) for all x,y, [0,1], andf(0) 0. If y=y(x) satisfies the differential equation, =f(x) with y(0)=1, then y y is equal to
a.
4
b.
3
c.
5
d.
2
Let f : [0,1] R be such that f(xy)=f(x).f(y) for all x,y, [0,1], andf(0) 0. If y=y(x) satisfies the differential equation, =f(x) with y(0)=1, then y y is equal to
|
a. |
4 |
b. |
3 |
|
c. |
5 |
d. |
2 |
1 Answer
127 votes
Answer Key / Explanation : (b) -
f(xy)=f(x).f(y)
f(0)=1 as f(0)
0
f(x)=1
= f(x)=1
y = x+c
At, x=0, y=1
c=1
y=x+1
y
y 
+1+
+1=3
127 votes
Answer Link
127