4) Consider the equation (2x? – 3x – 8)y" + 4xy' – y = 0. A solution to this equation is y(x) = > bn (x – 1)" n=0 for some constants b, , E 0,1,2, .. Find the minimum interval of convergence for y(x).

Q: f (x )² – 1 When the function f(x) satisfies f(1) =1,f'(1)=3 obtain a value of lim x→1 - 1

A:

Q: Find X(S) usng the following 1 |difforen tial oguetion X(0) = 4 x"- 2x' +x = et f(4)

A:

Q: f (x) = 2x+7 if -5=Xcl 8 If X = 1 14X=3 if 11x-2 31 If x > 3 IS this continuous at X=1 ? formula…

A: Any function f(x) is continuous at x=a if  lim x -> a f(x) = f(a) i.e. Functional value at that…

Q: FIND M'(3) = Page 2 of 4 -1 6 2 g(x) • F(x) LET M (x) = F (g(x)) AND V(x) = 9 (f(x)) 6 FIND V'(3) =

A: Step 1: Step 2: Step 3: Step 4:

Q: dy = ay + by", dt a > 0, 6 > 0, -∞ < Yo < ∞

A: A differential equation is given by, dydt=ay+by2 for a&gt;0, b&gt;0, y0&gt;0. The objective is to…

Q: A) At x=-1, y" is negative, concave downward, hence, y (-1) is a relative maximum value. B) At x=3,…

A: To solve the following problem

Q: x-1 pose g(x) Find the value of x in the interval 1, o0) where g(x) takes on its maximum value.

A: Given query is to find the the value of x where g(x) will be maximum.

Q: (10) Total number of items sold during a year is N(t) = t v4+t where N is in thousands and t is the…

A: Given function is, N(t)=t4+t where N is in thousands and t is the number of months since the…

Q: Using Reduction to an equation whose Right Member is zero: (D² + D)y= == COSX

A:

Q: In a new suburb, it is estimated that the number of registered voters 3. will change according to 3b…

A:

Q: Suppose that the net energy generated by a solar panel in a small town up to time t in a day…

A:

Q: Given the function f(x) = 1/2x4 – x3 – 2,

A: Given function is fx=12x4-x3-2     .....1

Q: Given f''(x) = 8x + 6 and f'(0) = 1 and f(0) = 2. Find f'(x) =

A: f''(x)=8x +6integrating w.r.t. x;∫ f''(x) dx =f'(x)f'(x) =∫ (8x+6) dx        =8x22+6x+Cf'(x)…

Q: 2r + 9(x)+ sin(rx). (2) Let f(x) = g where g is a differentiable function such that )-1-4 ) - d(1) =…

A: Given: f(x)=g(2x+12g(x)+sin(πx))g(14)=1−22=1−12g'(14)=2π2=π2g'(1)=3f'(14)=?

Q: (a) Find the roots of the function, f(r) = r – - 1, analytically up to 3 decimal places. (b) and…

A: (a) f(x)=x6-x3-1Let x3=yf(y)=y2-y-1Here a=1,b=-1,c=-1y=-b±b2-4ac2a  =1±1+42   =1±2.2362…

Q: Consider differentiable functions a(t), B(1), a, B: [lo, l₁] → R, and set µ(t) = a(t)+iß(t). Explain…

A:

Q: undetermind effients y-2y'+sy= e"cosaz CO522

A: The given equation can be written as (D2-2D+5)y=excos2x.               ⋯⋯1 Ley y=e^{mx} (m being a…

Q: A particle moves along the x-axis so that at any time t > 0, its acceleration is given by a(t)=…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3. Write an equation of a line that is parallel to y = 5 - %x

A: The line is given as y=5-23x   …(1) We have to find an equation of line that is parallel to the line…

Q: Jаx + 2 for x 3 Find b – a. (A) 5 (B) 6 (C) 11 (D) 17 O A ов O C D

A: Here we have to find the value of b-a.

Q: 5-s s² + 4s-5 (A) Find L¹(F(s)}, knowing that: F(s)=- DA

A:

Q: (10) Without finding T and N, write a(t) in the forma(t) = a-T + ayÑ at t= r(t) =

A:

Q: not Show that ([0,1]_is in the l' metric d (fig)= (51f6)-96) ³d x) ² fumpluts

A: The given set is X = C[0,1] and the metric defined on X is L2 metric which is defined as  df, g =…

Q: (2а — 4)° Let f(x) = Find f'(x). (ба + 3)° f'(x) =

A:

Q: (t²,0 2 7. in terms of unit step function, hence obtain LT. %3D

A:

Q: Find F

A: Given:

Q: Find the largest interval on which the LV.P (x +(4) x -5) y" + sin(x) y' + y =0, y(0)= 3, y'(0)=4…

A: