Given the differential equation y" - 3y' = &x2 + 7x – 11 Determine the Characteristic Equation for the given Differential Equation and then find its Solutions.

Q: Eliminate the arbitrary constants b2 x2 - a2y? = a²b? %3D |

A:

Q: x²+2 dx x+2

A: We can solve the integral as below.

Q: mber of these fish reached 90 thousand in the year whole number.)

A: Given: The number of a particular fish in thousand x years after 1974 can be modeled by f(x) = 223(0...

Q: What is the equation of the parabola with horizontal axis, vertex (-2,1), and passes through the poi...

A:

Q: Use a quick approximation to estimate the derivative of the given function at the indicated point. H...

A: We know that d/dx(xn)=nxn-1

Q: Find the equation of the tangent to the graph at the indicated point. HINT [Compute the derivative a...

A: Given function is   f(x) = 7x + 1 To find the equation of the tangent at x=9. Now at x= 9 , f(x) = 7...

Q: Find u v. u = 4i - 3j v = i - j V U V =

A: Finding the dot product of u and v

Q: Question Evaluate the following limit using L'Hospital's rule. lim (x+ 6) In ( (æ + 6)² ) z-6+ Provi...

A: if the limx→af(x)g(x) is of the form ∞∞ then by L'Hospital rule the limit is equivalent to limx→af(x...

Q: 13 – 2r dx 1.

A:

Q: QUESTION 5 A conical water tank has a radius of 5 cm at the top and 20 cm high as shown in Figure 1....

A: Given: A conical water tank has a radius of 5 cm at the top and 20 cm high.  Water flows into a tank...

Q: What is the equation of the directrix of the parabola X+2x+4y-27=0 2

A:

Q: Evaluate f"(e) when e = 0 given f (e) = 2 sec 30

A: Given that: f(θ)=2sec3θ

Q: A. Find the differential equation: (1) whose general solution is y = c,e-2x + Cze3x (2) by eliminati...

A: To find the differential equation.1 whose general solution is y=c1e-2x+c2e3x.2 by eliminating B and ...

Q: (2z+1 if z < 3 (10-z if z 2 3* 3. f(z) = a.7 (2z+1 if z<3 4. f(z) = 110 – zif z 2 3 a. 7 S2z +1 if z...

A:

Q: y = x², x = 1, y = 0; about the y-axis

A:

Q: tant dt. 1+ t2 F(x) = 1-2т

A:

Q: %3D cosx cotx sin x CSCX

A:

Q: f A is 3 × 3 and det(2A-1) = -3 = det(A³(B¯1)"), find det B. 32 a) 을 (b)을 (e) (d) (e)을 83 34 23 83 (...

A: Topic:- matrix algebra

Q: Solve in detailed solution A. Í (4x³+x) v4x²+1dx B. (x+2) Vx+3dx

A: Let I=∫(4x3+x)4x2+1dxI=∫x(4x2+1)4x2+1dxI=∫x(4x2+1)(4x2+1)1/2dx I=∫x(4x2+1)32dx Put (4x2+1)=udifferen...

Q: Let   f(x, y) = √y - 2x.              NOTE: The y - 2x is all under the square root!

A: fx,y=y-2x Since value under the root will be ≥0 So range of f will give square root of non negative ...

Q: Are there any points on the hyperboloid r2 - y? – 22 = 1 where the tangent plane is parallel to the ...

A: Given hyperboloid ;    x2-y2-z2=1  and equation of plne which is parallel to tangent plane  x+y-z=0

Q: (In(x))? 3

A: We have to apply rules of integration to solve the problem

Q: Find a parametrization of the circle of radius 7 in the xy-plane, centered at the origin, oriented c...

A:

Q: y'+ 3 y = 4 x y(0)= 3 Y(x)=|

A: We can solve the initial value problem as below.

Q: x(x* –1) dx x' +1

A: This integral is of expression a2 + x2 . 

Q: Beth is filling a small backyard pool with a garden 647. hose. The pool holds 30 gallons of water. A...

A:

Q: raph of a function is given. y hich x in the range shown is the function increasing? For which x is ...

A: Given query is to find the interval of value of x where function is increasing and decreasing.

Q: 3sin4t dt 2. 5(1- 3cos21)

A: We have to find integral

Q: "Jung Kook PROBLEM SOLVING" Jung Kook stayed at McDonald's and ordered a cup of hot coffee. When the...

A:

Q: e that the bacteria in a colony grow unchecked according to the Law of Exponential Change. The colon...

A:

Q: 14х10+8 еx F (x : 4 x' + 13

A: Given: fx=14x10+8ex4x+13

Q: 1. Find the limit of the following: x° – 11x +37x* +6x' – 297x? +621x – 405 lim. x* —11x* +47х* -114...

A:

Q: {k}, {I, m, o}, {n, p}} of the set U = {k, I, m, n, o, p}. Give the

A: Solution is attached below.

Q: se vectors to determine whether the triangle with vertices A = (1,–3,–2), = (6,–2, -5) is right-angl...

A: we know that if the dot product of two vectors is zero then the two vectors are perpendicular. there...

Q: e' sin 0 dy 8. de 7.3:8 Solve the differential equation y sec 0

A:

Q: Consider the vector function r(t)=⟨t,t^2,t^4⟩ Compute r′(t)=⟨  ,  ,  ⟩ T(1)=⟨  ,  ,  ⟩ r′′(t)=⟨  ,  ...

A:

Q: Consider the double integral •3 cos (a2) dx dy 3y COS

A:

Q: For what Values Of X IS tne wing geommetric series convergent? 1++ 27 1) x>0 2) -1<x<1 3) -3<x<3 4) ...

A: Topic:- series   

Q: A function F is an antiderivative of the function f on an interval I ifLfor all x e 1. (A) F(x) =f (...

A: A function F is an antiderivative of the function f on an interval I if 

Q: Let f (x, y) = 3y O 1 x/3 1/(3у) (1/3)y

A:

Q: Obtain the Taylor series expansion of the function f(x) = cot x centered at a 4

A:

Q: 22 – 11z + 28 Find the limit, if it exists: (Do not use L'Hospital's rule) lim 7 2 – 26x + 133 Note:...

A:

Q: 1- Solve the following equations using Grammar's rule: b) 2x + y - z = 2 x - y +z = 7 2x + 2y + z = ...

A: Given system of equation2x+y-z=2x-y+z=72x+2y+z=4We know that for system of equation a1x+b1y+c1z=d1a2...

Q: 2. Evaluate the following functions using the given relations. f(1) = 4 ; f(2)=-1; f(3) =-3 Given: R...

A: (2). Given:f(1)=4 ;        f(2)=-1 ;        f(3)=-3f(n+1)=5·f(n)2-2f(n-1)

Q: (a) What is the relative growth rate? Express your answer as a percentage. (b) What was the intitial...

A: Follow the procedure given below.

Q: 10 dS (3t2-12t-15)dt %3D

A:

Q: All parts of this problem refer to the function below. y = (9+ 6x)²/¤ dy a) Use logarithmic differen...

A: We have to find derivative

Q: 4 – 2x dx. x3 + 2x2

A:

Q: Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. ...

A: Our Aim is to determine whether the given sequence limn→∞ -8n!nn-(i)is convergent or divergent.

Q: Solve the following second-order differential equation: y" + 4y/ + 5y = 8x sin x

A: