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d^2y/-6 dy/dx+9y=1+x+x^2

Solve the following initial value problem


Ut(x,t)=10Uxx(x,t) -10

U(-1,t)=U(1,t) Ux(-1,t)=Ux(1,t) t>0

Ux(x,0)=x+1 -1



A String is stretched and fastened to two points l apart. Motion is started by
displacing the string in the form

Solve the differential equation by separation of variables with step-by-step procedures.

(x+2)dx = (x+3) siny cosydy


Solve the differential equation by separation of variables.


(x^3 + 2)y = x(y^4 + 3)y’ ; at x = 1 and y = 1


Suppose you discover an expired library book in the attic for which your great-great-grandfather owes a fine of 30c for 100 years. If a penalty owed grows exponentially at 5% per year in continuous compound interest, how much would you have? What to pay if you return the book today? Rta. 44.52


(D

3 − 3DD

′2 − 2D

′3

)z = cos(x + 2y)


Find the integral surface of (x-y)(p-q) = z(q+1) which contains the circle z=4; x2+y2=42.


For equation of y^2dy= x(xdy-ydx)e^(x/y)

1. Find the function M(x,y) and its degree
2. Find the function N(x,y) and its degree
3. Is the given Differential Equation a homogenous? If yes, what is the degree?

x sin y - y cos x = c



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