Search & Filtering
Determine the Green, s function and express the solution as a definite integral
-y''=f(x), y(0)=0, y'(1)=0
Determine the Green function and express the solution as a definite integral
-(y''+y)=f(x), y'(0)=0, y(1)=0
Find the eigen value and eigen function of homogeneous integral equation
y(x)= 𝜆"\\int"K(x,t)y(t)dt where K(x,t)= sinx sin(t-1) -𝜋<=x<=t
sint sin(x-1) t<=x<= 𝜋
A tank having a capacity of 1000 liters, initially contains 400 liters of sugar water having a concen-
tration of 0.2 Kg of sugar for each liter of water. At time zero, sugar water with a concentration of
50 gm of sugar per liter begins pumped into the tank at a rate of 2 liter per minute. Simultaneously,
a drain is opened at the bottom of the tank so that the volume of the sugar-water solution in the
tank reduces 1 liter per minute. Determine the following:
Find the general solution of the differential equation y" + 16y = 2 sec(4t) tan(4t)
Select one:
O none of the given answers is true
y = ci cos(4t) + c2 sin(4t) + ,t cos(4t) - sin(4t) In | cos(4t) |
y = ci cos(4t) + c2 sin(4t) - t cos(4t) + sin(4t) In | cos(4t) |
y = ci cos(4t) + c2 sin (4t) -
7t sin(4t) - - cos(4t) In | sin(4t) |
y = ci cos(4t) + C2 sin(4t) + ,t sin(4t) + - cos(4t) In | sin(4t)|
If yp = uj (t) cos(2t) + u2(t) sin(2t) is a particular solution of the differential equation
y" + 4y= csc(2t) cot(2t), then u, (t) =
Select one:
O none of the given answers is true
O Lt + - cot(2t)
O _ In | sin(2t) |
O
_ In | sin(2t) |
O
cot (2t)
4Uxx+5Uxy+Uyy+Ux+Uy=0
