STUPIDSID
1 (a)
Solve \[4\dfrac{d^{4}y}{dx^{4}}-4\dfrac{d^{3}y}{dx^{3}}-23\dfrac{d^{2}y}{dx^{2}}+12\dfrac{dy}{dx}+36y=0\]
6 M
1 (b)
Solve \[\dfrac{d^{3}y}{dx^{3}}+6\dfrac{d^{2}y}{dx^{2}}+11\dfrac{dy}{dx}+6y=e^{x}+1\] using inverse differential operator method
7 M
1 (c)
Solve (D2-2D)y=ex sinx using method of undetermined coefficients
7 M
2 (a)
Solve (4D4-8D3-7D2+11D+6)y=0
6 M
2 (b)
Solve (D2+4)y=x2+ex using inverse differential operator method
7 M
2 (c)
Solve (D2-2D+2)y=ex tan x using method of variation of parameters
7 M
3 (a)
Solve \[\dfrac{dx}{dt}-7x+y=0,\dfrac{dy}{dt}-2x-5y=0\]
6 M
3 (b)
Solve \[x^{2}\dfrac{d^{2}y}{dx^{2}}+4x\dfrac{dy}{dx}+2y=e^{x}\]
7 M
3 (c)
Solve y=2px+y2p3 by solving for x
7 M
4 (a)
Solve \[(1+x)^{2}\dfrac{d^{2}y}{dx^{2}}+(1+x)\dfrac{dy}{dx}+y=2\]sin (log(1+x))\]
6 M
4 (b)
Solve \[\dfrac{\mathrm dy}{\mathrm d x}-\dfrac{\mathrm dx}{\mathrm d y}=\dfrac{x}{y}-\dfrac{y}{x}\] by solving for P.
6 M
4 (c)
Solve (px-y)(py+x)=a2p by reducing to Clairaut's form.
7 M
5 (a)
From the function f(x2+y2,z-xy)=0 from the partial differential equation.
6 M
5 (b)
Derive one dimensional wave equation as \[\frac{\partial^2 u}{\partial t^2}=c^2\frac{\partial^2 u}{\partial x^2}\]
7 M
5 (c)
Evaluate \[\int_{0}^{1}\limits\int_{x^2}^{2-x}\limits xy\ \mathrm d y \ \mathrm d x\] by changing the order of integration
7 M
6 (a)
Solve \[\frac{\partial^2u}{\partial x\partial y}=\sin x\ \sin y for \ which\ \frac{\partial u }{\partial y}=-2 \sin y\]when x=0 and u=0 when y is an odd multiple of \[\dfrac{\pi }{2}\]
6 M
6 (b)
Derive one dimensional heat equation as \[\dfrac{\partial u}{\partial t}=c^{2}\dfrac{\partial^2u }{\partial x^2}\]
7 M
6 (c)
Evaluate \[\int_{-1}^{1}\limits\int_{y}^{y}\limits\int_{x+y}^{x-y}\limits\ (x+y+z)\ dydxdz\]
7 M
7 (a)
Find the area between the parabolas y2=4ax and x2=4ay using double integral
6 M
7 (b)
Evaluate\[\int_{0}^{1} \limits\dfrac{dx}{\sqrt{1-x^{4}}}\] using beta and gamma functions
7 M
7 (c)
Express the vector zi-2xj+yk in cylindrical coordinates
7 M
8 (a)
Find the volume of the solid bounded by the planes x=0, y=0, x+y+z=1 and z=0 using triple integral
6 M
8 (b)
Express \[\int_{0}^{\pi/2}\limits \sqrt{\sin \theta}\ d\theta \times \int_{0}^{\pi/2}\limits\dfrac{d\theta}{\sqrt{\sin \theta}}\] using beta and gamma functions
7 M
8 (c)
Express the vector field 2yi-zj +3xk in spherical polar coordinate system
7 M
9 (a)
Find Laplace transform of \[te^{-4t}\sin3t \ and \ \dfrac{e^u-e^{-u}}{t} \]
6 M
9 (b)
Using f(t) in terms of unit step function and find its Laplace transform given that
\[\left\{\begin{matrix} t^2, &04
\end{matrix}\right.\]
\[\left\{\begin{matrix} t^2, &0
7 M
9 (c)
Find \[L^{-1}\left \{ \dfrac{1}{(s+1)(s^2+9)} \right \}\] using convolution theorem
7 M
10 (a)
A periodic function f(t) with period 2 is defined by \[f(t)=\left\{\begin{matrix}
t, &0
6 M
10 (b)
Find \[L^{-1}\left \{ \dfrac{5s-2}{3s^2+4s+8}+log\left ( \dfrac{1} {s^2}-1\right ) \right \}\]
7 M
10 (c)
Solve using Laplace transform method \[\dfrac{d^2y}{dt^2}+2\dfrac{dy}{dt}+y=te^{-1}\ with \ y(0)=1,y^1(0)=2\]
7 M
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