* Lct X; ~ exp (2) · Show that T= EX, is Su fficient pro pesty of T %3D

Q: Find the solution of the differential equa­tion that satisfies the given boundary condition(s) . g"…

A:

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: Given that the function is  f(x)= e-x, a= -0.1 To determine the linearization for the function.  The…

Q: Given the first-order ODE dy -12y , dt Perform a linear stability analysis to find the amplification…

A: Given, dydt=-12yTo find: Amplification factor for the mid point method applied to given ordinary…

Q: Two equivalent forms of the Chain Rule for calculating the de-rivative of y = f(g(x)) are presented…

A: Given, if y=fx and u=gx then the derivative of their composition can be expressed as

Q: 1. Find the orthogonal trajectories of the family of curves x? + y2 = cy.

A:

Q: 16 – tª -dt t3 Integrate: + C

A:

Q: 4. Let A(x) = ſ dt. Find the local minima, local maxima, and t2+1 inflection points of A(x).

A:

Q: 5Find the Orthogonal trajectories of the family of r=aeº

A: Question:- Find the orthogorial trajectories of the family of r=aeθ ?Solution :- We have r=aeθ -(i)…

Q: Find y' for y = vTy at the point (9,1).

A: Given: y=xy ⇒y=x12y12 ⇒y12=x12

Q: 4. Find the orthogonal trajectories of the family of curves y= Ce“ + 10

A: Here we have to find the orthogonal trajectories

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: Given, f(x)=1x, a=0.9 now find linearization f(0.9)=10.9=109 so linearization at 910,109…

Q: y = x – 2 + Ce* X-

A:

Q: الموضوع was althe eauation XÝY-2* Ý+4.=2* is a Linear differential Eauation and Heterogenious Dtrue…

A: The given statement

Q: etermine the orthogonal trajectories for x? = ky³.

A:

Q: 4 Find the linearization of the function f (x) = x² at x = 1. L(x) = Using this linearlization, ƒ…

A: f(x)=x4 at x=1 So, L(x)=f'(1)(x-1)+f(1)

Q: [1] Determine the orthogonal trajectories of y(1+2x?)=ax.

A: The given equation is:y1+2x2=axy=ax1+2x2              ..............(1)

Q: What is the differential equation of the orthogonal trajectories of x3 = Cy? (1) Зxdx + 2уdy — 0 (2)…

A:

Q: Find the differential dy of the given function. y = 3x2 − 4

A: Given function is Differentiating with respect to x, we get Therefore , differential dy is

Q: 2. Using Euler's method with N = 8 and 10. dx/dt = 1 + tsin(tx), x(0) = 0

A: Given dxdt=1+tsintx  and x(0)=0 and N=8, N=10

Q: 4. Find the general form of the function that satisfies dP/dt = -3P(t).

A: A separable differential equation can be solved by separating the terms in each variable and…

Q: Find the orthogonal trajectories of the following family: y = Ce-x

A: First differentiate then  solve

Q: Use variation of parameters to find a particular solution of the ODE y" – y = 2e".

A: Given differential equation is  y''-y=2ex we have to find  the particular solution of this…

Q: fCx)=(1+x)* at X=0 is LUX)=1+ KX + "७) %3

A:

Q: Find the particular soluti y' + 3x²y = 3x² %3D Initial Condition: y = 6 %3D

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Q: The partial differential equation is classified as a. hyperbolic b. elliptic c. elliptic / parabolic…

A:

Q: Consider xy' = y(lnx-lny) with y(1) = 4. Using Runge-Kutta method with h-0.1, approximate y '(1.3).…

A: option c is correct i.e. (c) -1.92711

Q: Find the orthogonal trajectories of x² + y² – 2cy = 0

A:

Q: Q1: Use ewton- Raphson method to estimate the Yoot of fcx) = x -x -1 , emp loying an initial %3D…

A:

Q: find the integrating factor of the given linear DE and general solution of the y'+1/x (y)=cos(x)

A: Consider the given linear differential equation. y'+1xy=cosx The objective of the problem is to find…

Q: Find the linear approximation to h(x) = Vx at x = 2. Use the linear approximation t approximate the…

A: Introduction: The linear approximation of a function at a given point is an application of…

Q: S(«,9) =7+3y Also, find the total differential of the function.

A:

Q: Suppose that a body moves through a resisting medium with resistance proportional to its velocity v,…

A: (a)

Q: Suppose P is a linear differential operator that factors but has variable coefficients. Do the…

A: If P is linear  differential operator that factors but has variable coefficients ,

Q: The ops y' =esx-7Y;s Separable

A:

Q: Find the linearization L(x) ofy = e8# ln(x) at a = 1. L(x) =

A: We will use formula for linearization at one variable.

Q: [1] Determine the orthogonal trajectories of y(1+2x²)=ax.

A: The given equation is:y1+2x2=axy=ax1+2x2              ..............(1) Determine the orthogonal…

Q: nake/s the DE nonlinear y' =1-xy+ y2

A:

Q: 27. Find the length of the curve Vcos 2t dt y = from x = 0 to x = "/4.

A: The given curve is We know that by Second Fundamental theorem of calculus ,if F(x) is continuous on…

Q: Let = f(x,y) = x² -y. Use Euler's method ( with step size h = 1) to approximate the value of y(2) if…

A: The Euler method is a first-order numerical procedure for solving ordinary differential equations…

Q: 4. Find the orthogonal trajectories of the family of curves y= Ce“ +10

A: Given that, Family of curves is following, y = Ce2x + 10…

Q: Let A and k be positive constants. What is a solution to dy/dt=k(1-Ay)

A:

Q: a Find the Orthogonal trajectories of the family of r =; 1+coso

A: we need to find the orthogonal trajectories of the given family of the curve in the polar form.

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: Given: f(x)=1+3x-5x3

Q: For the family x² + 3y2 = c, find that member of the orthogonal trajectories which passes through…

A:

Q: x2 - y2 + 2Cx = 0

A:

Q: Estimate v16.3 using the linearization L(x) of f(x) = /x at a = 16. (Use decimal notation. Give your…

A:

Q: 8. Find the orthogonal trajectories of y cx

A:

Q: Find the linearization L(x) of y = e6« ln(x) at a = 1. L(x) =

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.