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

(a)

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

(b)

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

(c)

log x

(d)

x

The particular integral of the differential equation f(D)y = e^ax where f(D) = (D−a)² ______.

(a)

\(\frac { { x }^{ 2 } }{ 2 } { e }^{ ax }\)

(b)

xe^ax

(c)

\(\frac { x }{ 2 } \)e^ax

(d)

x²e^ax

The P.I of (3D² + D − 14)y = 13e^2x is ______.

(a)

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

(b)

xe^2x

(c)

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

(d)

13xe^2x

A homogeneous differential equation of the form  \(\frac { dx }{ dy } \) = f\(\left( \frac { y }{ x } \right) \) can be solved by making substitution,______.

(a)

x = v y

(b)

y = v x

(c)

y = v

(d)

x = v

The solution of the differential equation \(\frac { dy }{ dx } =\frac { y }{ x } +\frac { f\left( \frac { y }{ x } \right) }{ f'\left( \frac { y }{ x } \right) } \) is ______.

(a)

\(f\left( \frac { y }{ x } \right) =k.x\)

(b)

\(xf\left( \frac { y }{ x } \right) =k\)

(c)

\(f\left( \frac { y }{ x } \right) =ky\)

(d)

\(yf\left( \frac { y }{ x } \right) =k\)