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Find the Laplace transforms of
f(t)={4,0<=t<=1
{3,t>1.
(d^2y/dx2)-2(dy/dx)+2y=sin2x

Find the Laplace transforms of

1.(t^2 e^2t)

2.[1+e^(-t)]^3

3. [t√(1+sin t)]



The differential equation of a family of tangent lines to the parabola y=x^2, given by 2xt=y+t, t being a parameter,4(y-xdy/dx)+(dy/dx)^2=0.
True or false with statement
A steel Ball weighing 39.2 kg is supposed from a spring due to which the spring is stretched 2m from its natural length. The ball is started in motion with no initial velocity by displacing it through 0.5m above the equilibrium position. Assuming no air resistance, find an expression for the position of the Ball at any time t.
write short note on higher order differentia ability
state and prove existence and uniqueness theorem
The general solution u(x,t)=(A sin pcx +B cos pcx )(C sin pct+D cos pct ) with u(0,t)=0 and u(l,t)=0 gives..........

find the partial differential equations arising from z=xy+f(x^2+y^2)


 (3-y)/x^2  dx+(y^2- 2x)/(xy^2 ) dy=0        y(-1)=2


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