QUESTION $1$

Solve the following first order differential equations:

$1\mathrm{.}1\frac{dy}{dx}-(\frac{y}{x})=2(\frac{y}{x})$

$1\mathrm{.}2x\frac{dy}{dx}+y=y^2{x}^3{e}^{2x}$

$[16]$

QUESTION $2$

The motion of a vibrating mass is given by $x(t)+9x(t)=6sin3t.$ Find the general solution for the motion $x(t)$ using the method of undetermined coefficients.

$[10]$

QUESTION $3$

Find the general solutions of the following differential equations using D$-$operator methods:

$3\mathrm{.}1(D-2{)}^{3}y=60e^{2x}{x}^2$

$3\mathrm{.}2(D^2-3D+2)y=sinx$

$[14]$

QUESTION $4$

Solve for $x$ in the following set of simultaneous differential equations by using D$-$operator methods:

$(D-3)x,+y=-1$

$-x+(D-1)y=4e^t$

$[10]$

QUESTION $5$

Determine the following:

$5\mathrm{.}1L\{e^{3t}(t^2+4)\}$

$5\mathrm{.}2L\{2sin(2x)cosh(2x)\}$

$5\mathrm{.}3,L^{-1}\{\frac{s-5}{s^2+4s+20}\}$

$[10]$

$[$Page down$]$QUESTION $1$

Solve the following first order differential equations:

$1\mathrm{.}1\frac{dy}{dx}-(\frac{y}{x})=2(\frac{y}{x})$

$1\mathrm{.}2x\frac{dy}{dx}+y=y^2{x}^3{e}^{2x}$

$[16]$

QUESTION $2$

The motion of a vibrating mass is given by $x(t)+9x(t)=6sin3t.$ Find the general solution for the motion $x(t)$ using the method of undetermined coefficients.

$[10]$

QUESTION $3$

Find the general solutions of the following differential equations using D$-$operator methods:

$3\mathrm{.}1(D-2{)}^{3}y=60e^{2x}{x}^2$

$3\mathrm{.}2(D^2-3D+2)y=sinx$

$[14]$

QUESTION $4$

Solve for $x$ in the following set of simultaneous differential equations by using D$-$operator methods:

$(D-3)x,+y=-1$

$-x+(D-1)y=4e^t$

$[10]$

QUESTION $5$

Determine the following:

$5\mathrm{.}1L\{e^{3t}(t^2+4)\}$

$5\mathrm{.}2L\{2sin(2x)cosh(2x)\}$

$5\mathrm{.}3,L^{-1}\{\frac{s-5}{s^2+4s+20}\}$

$[10]$

$[$Page down$]$