Which of the given models may explain a real life process involving limited growth { * = ky, k >0 { = ay, a < 0 y (0) = c, c>0 ' I : II y (0) = c, c> 0 * = k (M – y), k, M > 0 y (0) = 0 * = ky (M – y), k, M > 0 IV : III y (0) = ¥ O A)I, II, and IV O B)|l and II O C) Ill and IV O D) Il only O E) IV only

Q: d. yy'- y = 6 e*, y(0) = 1 %3D е. %3D %3D

A:

Q: Y"'-y"+y'-y=xe^x-xe^-x+7 By using variable cofficients

A: Given differential equation is y'''-y''+y'-y=xex-xe-x+7 Now auxiliary equation is…

Q: xy^(2)y' = x^(3) + y^(3)

A:

Q: Evaluate y'' + 3y' + 2y = e^-t  When, y(0) = 4 and y'(0) = 5

A:

Q: y'''+y''=3 (Non Homogenous DE)

A: y'''+y''=3 (Non Homogenous DE)

Q: Differentiate y = ex+2 +9.

A: Given function is y=ex+2+9 We need to find the first derivative of the given function.

Q: 2) y' – (cotx)y = -(2cosx)y2 %3D

A:

Q: -pf'(p) Let q = f(p) be the demand function for a certain commodity, where q is the demand quantity…

A: Given q=f(p)E(p)=4p+1E(p)=-pf'(p)f(p)

Q: e'y' = e + 4x, y(1) = 5. %3D y =

A: First we convert the given differential equation into an exact differential equation by multiplying…

Q: y" + y' = xe" denkleminin ÖZEL ÇÖZÜMÜ hangisidir? O a. yp=(1/2)e^ (3x).[x-(3/2)] O b. yp=…

A: The given differential equation is  y" + y' = xex

Q: xyy' = x^2 + 2y^2; y(1) = 3

A:

Q: et ● t'(x) = 805x4 (x),1 O %3D O t'(x) = 80(e)-(e*)(5x4) (x),1 e2r e2x ((*(-(,r5)(,2) 08 = (x),1 C…

A:

Q: Determine y' when y = x-1/x 1. y' y (lnx + 1) 2. y'= -ry(2 ln x + 1) 3. y' ry(2]nr−1) 4. y = −…

A:

Q: evaluate y"+5y'+6y=0    if y=e^-3t, y'=-3e^-3t, y"=9e^-3t

A:

Q: The profit from the sale of a certain product is increasing at a rate given by P'(x) = 970x1/3,…

A: To find P(x) we have to integrate P'(x)

Q: Ex. 8 Differentiate k(x)= ln(x)f(x)

A: Our AIm is to differentiate the function given below:-f(x)=ln (x) f(x) -(i)

Q: y''+4y=0  y(0)=5 , y'(0)=6 find the start and end values Y(s)=?

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Q: (d) y = x/1 (e) y = e", y = e3, and x = 1 (f) u = 2" , y = 5", and x= 1

A:

Q: Simulate the segmental growth problem: a -(1+q)a, – ra = 0,a, =1, try various 'n+1 'n-1 values for q…

A:

Q: y" - y' - 2y= e* %3D

A:

Q: 13. y" + 3y' +2y=6_y(0)=1 _y'(0) = 2

A: y''+3y'+2y=6y0=1y'0=2

Q: 1.) xy3dx + (y+1)e^-xdy = 0 2.) dx/dy = x-2ycotx

A:

Q: y''+y=e^x sin(x) y(0)=1    y'(0)=0

A:

Q: y' + 4y = e^(4t) %3D

A:

Q: The equation of the tangent line to f(r) = at z = 1 is y = ar +b and the tangent point is (1, c).

A:

Q: Suppose that y' = 4 – 3x – x² and y(0) = 0 Sketch the graph y = f(x) Make sure you label all local…

A:

Q: If y" = 1 (x + 1)² y(0)=2 y'(0) = 1 then y'= and y=

A:

Q: Solve for k:  y(t) = y(0) * e^(kt* (1-t/p) )  (we know that y(0)=P/10)

A: We have given yt=y0·ekt·1-tp,  y0=p10 By dividing both sides of the equation by y(0), yty0=ekt·1-tp…

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.