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Find out a series solution for the following differential equation about x 0 = 0 y′′ + y = 0. Solution Note that in this case p(x)=1 and therefore every point is an or
how does proportionality work
Two tanks initially contain 100 liter liquid each. Their initial concentration are listed in the Figure below. At time zero, the input and output valves are opened simultaneously w
Determine all possible solutions to the subsequent IVP. y' = y ? y(0) = 0 Solution : First, see that this differential equation does NOT satisfy the conditions of the th
Simplify the logical expression X‾ Y‾ + X‾ Z + Y Z +Y‾ Z W‾ Ans: The K-Map for the following Boolean expression is described by the following diagram. The optimized expression
Finds out the center & radius of each of the following circles & sketch the graph of the circle. a) x 2 + y 2 = 1 b) x 2 + ( y - 3) 2 = 4 Solution In all of these
Example of Integrals Involving Trig Functions Example: Estimate the following integral. ∫ sin 5 x dx Solution This integral no longer contains the cosine in it that
Linear Equations We'll begin the solving portion of this chapter by solving linear equations. Standard form of a linear equation: A linear equation is any equation whi
if A be the area of a right triangle and b be one of the sides containing the right angle, prove that the length of the altitude on the hypotenuse is 2Ab/rootb^4+4A^2
1/a+b+x =1/a+1/b+1/x a+b ≠ 0 Ans: 1/a+b+x =1/a+1/b+1/x => 1/a+b+x -1/x = +1/a +1/b ⇒ x - ( a + b + x )/ x ( a + b + x ) = + a + b/ ab ⇒
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