Jsing MOSA find the polynomials that will approximate the solution to: y' = x2 + y; y(1)=1.

Q: 3. (a) Determine f 2xe3*dx by using integration by parts. (b) Determine S cos(x²) 2x dx by using…

A:

Q: Express the general solution in terms of Bessel functions: z²y" + 4xy/ + (x² + 2)y = 0

A:

Q: Find the differential dy of the given function.

A: Given :              The given function is :                   y = 9 - x2 To find :            The…

Q: 2. Given So S√x y² +8 dydx. Reverse the order of integration and evaluate. Draw the

A:

Q: Find the antiderivative of xe2x/(1+2x)2 from 0 to 1/2

A: Given the integral ∫012xe2x1+2x2dx

Q: 2. Eliminate the arbitrary constants: x²y = 1 + Cx 1 Add File 3. Obtain the differential eguation of…

A:

Q: Given f(x) = 8x3 + In(x – 1). Estimate the value of f(2.01) using differential. %3D

A:

Q: 2. Express the general solution in terms of Bessel functions: 4x²y" – 4xy/ + (16x² + 3)y = 0

A:

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

A:

Q: 1. Find the differential dy in y= 2x4-3x3-5x 2. Use differentials to find approximate values for…

A:

Q: Perform the indicated multiplication on the differential operator D. Show your full solution.

A: We have to find out

Q: Is this polynomial, x In x – y In y - a homogeneous differential equation?

A:

Q: find a linear differential operator that annihilates the given function. y = x sin(3x)+ 3xe6x

A:

Q: y' – y = 2te',

A: Laplace transform: L(y'(t))=py(p)-y(0) L(y(t))=y(p) L(2tet)=2(p-1)2

Q: Express the solution of the equation 4.x²y" – 8xy' + (5 + 64/x*)y = 0 in terms of Bessel functions.…

A: Use the Bessel equation,  x2y"+1-2dxy'+β2r2x2r+d2-n2r2y=0  Identify the values of unknowns.

Q: Find the general solution for y''=2t+3 by direct integration and by the method of undetermied…

A: Given that      y" = 2t + 3 Here we have to find the general solution by direct integration and by…

Q: Determine an integrating factor and solve the followir xdy-ydx-(1-x')dx = o 1.

A:

Q: Solve the separable equation using the integral factor  y⁴ y¹ +y¹ + x² + 1 = 0

A: Given equation is y4y'+y'+x2+1=0solve it

Q: What is the general solution of the following ODE y' - (2y/x) = 3x3 Hint: Use integration factor…

A:

Q: Find the linear approximation of f(x) = ln x at a = 1 and use it to estimate In(1.2). L(x) = In(1.2)…

A:

Q: 5. Use the properties of differential operators to solve for the product of (D+x²)(xD + 2)y

A: Given: D+x2xD+2y To find: Solution

Q: Find the differential dz of the function f(z, y) = 4g²+z*y – 2xy and use it to approximate Az at…

A: Consider the given information:

Q: integral from 1 to 2 of (e1/x^3 ) / x4

A: To evaluate

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: Q2// FIND THE GENERAL SOLUTION WHEN THE DIFFERENTIAL EQUAION IS ỳ + 3ỳ + 2y = 36xe* %3D

A: Given the equation y''+3y'+2y=36xex Which is in the form of y''+py'+qy=s so, p=3, q=2 and s=36xex It…

Q: 2x 1. y =-+ 5 3 2. y = x6 + x³ + 5x – 8

A: The given functions are polynomials . we will find differential or derivative of the functions.

Q: Use the method of reduction of order to find a second independent solution of the given differential…

A: Use reduction of order method

Q: v = ) V In(2x-3y

A:

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

A: Simplify the given function by squaring the expression inside the parentheses.…

Q: Find the general solution using Reduction of Order: y''+y'=cos 3x

A:

Q: Find Lf 0- £{[ e-axdx } by transforming e atu(t) then applying the integratiori property

A: Given :I=∫0te-axdx Laplace Transform u(t)→ℒu(t)us=∫0∞e-stu(t)dt we need to find: ℒ∫0te-axdx

Q: What is most nearly the magnitude of the maximum error in the linear interpolation of the polynomial…

A: Given function is yx=cosx

Q: Assume that y is a function of x and use the integrating factor method to solve the differential…

A:

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

A:

Q: A 1125 m³ open-top rectangular tank with a square base x m on a side and y m deep is to be built…

A:

Q: Find the most general antiderivative of f(x)=−7x^2+8x−2. Note: Any arbitrary constants used must be…

A: An anti derivative of a function f is a differentiable function, whose derivative should be equal to…

Q: d*y dr -y = 8(x – a); dx4

A: Differential equation is an equation that represents the relation between variable and their…

Q: y" +y' = cos 3x

A:

Q: What are the roots of the characteristic polynomial for the differential equation y" + 4y' – 5y = 0?

A: Given differential equation:-   y" + 4y' -5y = 0

Q: Eliminate the arbitrary constants x = -ln t , y = at + bt^2

A: given  x=-ln t , y=at+bt2 claim- to eliminate the arbitrary constants

Q: The differential operator D4 annihilates the functions

A: we have to find the functions which are annihilated by the differential operator D4…

Q: - ydx + (x ++xy )dy= 0

A:

Q: Use the eliminatiun methoel t. 2こhoxet,htX differential equations

A: We can write the given system of differential equations as below: 2D-1x+D-1y=e-tD+2x+D+1y=et We have…

Q: 3. Find the general antiderivative of f(x) = x² + 3x+4 sinx.

A:

Q: find the general solution of the differentialequation and check the result by differentiation.dy/ dt…

A: The given differential equation: dydt=x32 Integrate both sides of the differential equation with…

Q: prove using the IVT. e^x + ln x = 0 has a solution.

A:

Q: Find the general solution using Reduction of Order: x2y''-xy'+y=0 y1=ln x

A: