The degree of the differential equation \(\frac { { d }^{ 4 }y }{ { dx }^{ 4 } } { -\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 4 }+\frac { dy }{ dx } =3\) ______.

(a)

1

(b)

2

(c)

3

(d)

4

The differential equation \({ \left( \frac { dx }{ dy } \right) }^{ 3 }+2{ y }^{ \frac { 1 }{ 2 } }\) = x is ______.

(a)

of order 2 and degree 1

(b)

of order 1 and degree 3

(c)

of order 1 and degree 6

(d)

of order 1 and degree 2

If y = cx + c− c³ then its differential equation is ______.

(a)

\(y=\frac { dy }{ dx } +\frac { dy }{ dx } -{ \left( \frac { dy }{ dx } \right) }^{ 3 }\)

(b)

\(y={ \left( \frac { dy }{ dx } \right) }^{ 3 }=x\frac { dy }{ dx } -\frac { dy }{ dx } \)

(c)

\(\frac { dy }{ dx } +y={ \left( \frac { dy }{ dx } \right) }^{ 3 }-x\frac { dy }{ dx } \)

(d)

\(\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } =0\)

The particular integral of the differential equation is \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -8\frac { dy }{ dx } \) + 16y = 2e^4x ______.

(a)

\(\frac { { x }^{ 2 }{ e }^{ 4x } }{ 2! } \)

(b)

\(\frac { { e }^{ 4x } }{ 2! } \)

(c)

x²e^4x

(d)

xe^4x

The integrating factor of x \(\frac { dy }{ dx } \) - y = x² is ______.

(a)

\(\frac {-1}{x}\)

(b)

\(\frac {1}{x}\)

(c)

log x

(d)

x