#@3 g (x; y) = 7x3 - 49IXY + 7y3 Find and elassify all the extreema of the fine tion

Q: d Using the Chain Rule Twice Calculate 1+ Vx2 + 1. dx

A: Given function is 1+x2+1

Q: 3.2.10 Example: By method of contour integration, prove that dx = t /4 (1+ x }

A:

Q: at Solve thie équation use Eulers methoc- ds -t X-ツ dx x+y y(6)%=1

A:

Q: 2 y

A: According our guidelines i solve only first question.For second solution please resubmit again…

Q: y)dx

A:

Q: Q3\ using Euler method, find an approximate value of y corresponding to x€ [0 -0.7], Given = x(x +…

A:

Q: Integrating Factor by Formulas: (7) xy³dx + (x²y² + 1)dy = 0

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Q) Use the chain rule to express dy / dx in terms of x and y for the :following y =1-! 1 t = 1-x and…

A: Consider: y=1-1t and t=11-x. Calculate dydxin terms of x,y at x=2. Calculate dydt and dtdx using…

Q: supposed that a drop of mist is a perfect sphere and that, through condensation, the drop picks up…

A:

Q: Solve ODE for general solution: (2ysin(x)cos(x)-y+2y^(2)e^(xy^2))dx=(x-sin^2(x)-4xye^(xy^2)dy

A: Hence the given ode is exact. Obtain the general solution as follows,

Q: 18 dx Integrate using trig. Substitution: S- x² V9– x²

A:

Q: 4) S(x, y) = (4x-x* )cos(y) on the Ans. Absolute max.: 4 at(2,0) 3/2 Absolute min.: at 2 rectangular…

A: Given

Q: Only I method. Except Exact DE (x+2y-1)dx+(2x+4y-3)dy oo

A: First we campare the given differential equation Mdx+Ndy= 0 and then solve it.

Q: Q3 (d^2 y)/(dx^2) - 2dy/dx of Undetermined Coefficient) 20e^(-x) cos(x), y(0) = 0 = y'(0) (Use…

A: we have to solve given differential equation by using method of undetermined coefficient

Q: y = x - 2 sin(x), 0 sxs 27 aximum value inimum value

A:

Q: 2- Linear edluan 1 - y' +スリ= 2é 2- x y'ony-ax? %3D 3. (x-2) y`+y. x 4 4-(49-3x)dX+5X dy = - 5_ dy dx…

A:

Q: kx 4+x² If k 1, evaluate k (a) 2 kx (b) 2 J₁ arctan (2x) + C arctan (2x) + C dx. (c) // ln(x² + 4) +…

A: Given: ∫kx4+x2dx We have to evaluate the given integral.

Q: 3. Obtain the Particular Solution when x = 4 and y = 1 (x+ y - 4)dx – (3x- y – 4)dy = 0

A:

Q: Find dy/dx if ylnx + y^2 = 0.

A: According to our guidelines, we can answer only one question or three subparts of a question.

Q: 2 4) d?y |1+ () dx2 dx, Find the: Туре: Order: Linearity: Why?: Unknown Function: Independent…

A: Topic:- differential equations

Q: 1. Obtain the General Solution. Use reduction to exact. Simplify your fin y(y + 2x- 2) dx - 2(x +…

A:

Q: Question The approximation of fxln (x + 5) dx using two points Gaussian quadrature formula is:

A:

Q: Solve the DEQ given the initial condition (2,0). Graph it on the slope field. 11 « 10 Let…

A: dydx=g(x,y)g(x,y)=ey(3x2) - dydx=ey3x2Separating the…

Q: 90% of it Suppose dy/dx = x-y and y = 2 when x 1, Use Euler's Method with increments of Ar = -0.1…

A: Given the differential      dydx=x-y with y(1)=2. Find y(0) using Euler's method with step size…

Q: 5. Find the particular solution (IVP) for the DE below: a) dx +2 =8x when x = 2, y = 6 b) 3y2 = 2x +…

A: Use variable separable method

Q: b. y = cosh(arctan 3x) C. y = 4a/ cosh a d²y d. for x = 4v2t2 + a, y = a² – t² dx2 %3| -

A: Given functions are  b) y=cosh(arctan3x) c) y=4acosha d) d2ydx2 for x=42t2+a , y=a2-t2

Q: order differential coefficients as serie (b) y) when y = (7) sin 50. 50

A:

Q: An electrical potential at a point (x,y) on the line segment extending from (0,3) to (2,0) is given…

A:

Q: 2. t23* dt

A: The given problem is solved below in detail.

Q: (12z – 12z2 + 71z – 77 Integrate: 4x2 + 25 - la( |42° + 25|) – arctan X + C

A:

Q: Solve by integrating factors found by inspection: y (x2 - y2 + 1)dx - x (x2 - y2 - 1) dy = 0

A: To solve: y(x2 - y2 + 1)dx - x(x2 - y2 - 1)dy = 0 ⇒yx2 dx- y3 dx+ y dx - x3dy +xy2dy +xdy = 0

Q: sin(2t + ) dt e21-3 4 7 4 4 64e 7

A:

Q: 17. Using Runge-Kutta method of fourth order, solve dy y2-x2 dx y2 + x2 | with y(0) = 1, at x = 02…

A: Numerical methods: Ruge-kutta method

Q: 3. Obtain the Particular Solution when x = 4 and y = 1 (x+ y - 4)dx - (3x- y – 4)dy = 0 %3D

A:

Q: Solve the disfertial equation xy' -Y =Xtan ) %3D

A:

Q: 3. (1−x³) d²y dx² DE -+ (sin x)y' − 3xy = ln x(+1) TYPE ORDER DEGREE LINEARITY

A: Need to write down the type, order, degree and linearity of the given differential equation.

Q: 4a 2vax Change the order of integration and evaluate " La xy dy dx 4a 4ax

A:

Q: Q1: Find the Integration using Gamma Function Method: x*e-3xdx 0.

A:

Q: 6) S sech? (2x- 3) dx | ex-e-x 7) S ex+e-x 8) S(eax – e-ax) dx sinh x 9) S dx 1+cosh x 10) ſ csch? x…

A: Given

Q: ;+ 2リ+y = ハ- cos(t) Slove the D- E t2 with. Ze Vo initial cuudition s En gineer ing Analysis

A:

Q: #@3 g (x1y) =- 7x3 -49xy + 7y3 Find and elassify all the extrema of the fine tion

A: Given- gx,y=7x3-49xy+7y3 To Find- All the extrema of the above function. Concept Used- Using the…

Q: Solve using separation of variables xy^2 dx + e^x dy = 0; when x -> infinite, y -> 1/2.

A:

Q: HX T-Th HY 3)1+2 2. 14 the eavation

A:

Q: 2EValuatethe Valee ofthe Inextintegration byusing the t rapezoidat vule zhen find the absotute…

A: Given that, ∫03π20sin5x+1dx with n=4

Q: Let y'=sinxy and y(0)=2 Approximate y(4) using Euler's method with step sizes of .25

A: The solution of a differential equation is defined as the function that satisfies the differential…

Q: +5y = sin x, y(0.3)=5 and using a step size of h = 0.3, Approximate the value of y(0.9) dx 2. %3D…

A: Given 3dydx+5y2 = sinx with y(0.3) = 5, h = 0.3

Q: A stone is thrown into a body of still water and created ripples in the form of concentric circles.…

A:

Q: V4-x² E Evaluate the double integral (x² + y² )°dydx.

A: Convert Cartesian coordinate system into polar coordinates system.