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Mathematics
Mathematics
Problem
The functions
u
=
e
x
sin
x
u = e^x \sin x
u
=
e
x
sin
x
,
v
=
e
x
cos
x
v = e^x \cos x
v
=
e
x
cos
x
satisfy the equation a.
v
d
u
d
x
−
u
d
v
d
x
=
u
2
+
v
2
v \frac{du}{dx} - u \frac{dv}{dx} = u^2 + v^2
v
d
x
d
u
−
u
d
x
d
v
=
u
2
+
v
2
b.
d
2
u
d
x
2
=
2
v
\frac{d^2u}{dx^2} = 2v
d
x
2
d
2
u
=
2
v
c.
d
2
v
d
x
2
=
−
2
u
\frac{d^2v}{dx^2} = -2u
d
x
2
d
2
v
=
−
2
u
d. All of these
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