For functionf (x, y) = e*y + cos(x – y), write the first and second order full differentials

Q: Given the differential equation of the family of circles with radius of 2 units and whose center's…

A: The equation of a circle is x-a2+y-b2=r2. Here, the center is a, b and radius is r. The abscissa is…

Q: Determine whether the differential equation is separable. y' (8x+y) c Cos O Separable Not separable

A: Given query is to find that differential equation is separable or not.

Q: find the differentials of the first and second orders u=xyz

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Q: List the six orders in which the three differentials dx, dy, and dz may be written.

A: First type= (dx)(dy)(dz) Second type=(dx)(dz)(dy) Third type=(dy)(dx)(dz)

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

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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: Show that the solution, of the differential 5x3 is of у — ху? — х*у dy equation: dx xy² – x²y – 2r³…

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Q: z = x siny + y sinx

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Q: Given the differential equation of the family of circles with radius of 2 units and whose center's…

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Q: Show that y, = x* – x² Inx over the interval (0, 0) is the particular solution to the…

A: (C) Given differential equation is x2y''−4xy'+6y=2x4+x2....1 We have to find the particular solution…

Q: Find the values of the constant r so that y = e™* satisfies the differential equation 2y" + y' — у…

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Q: Prove that the change in the dependent variable z = g´(y) transforms the equation in a linear…

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Q: For the differential equation x ^ 2y ”+ xy’ + y = 0, check that y1 = cos (lnx) is a solution. Find…

A: According to the chain rule of differentiation, the differentiation of the composite function…

Q: let (xev/x. y) dx – x dy=0 which is a homogeneous differential equation.

A: Given:

Q: 3. Write the exact differential: f(x,y)=e-y-el-

A: Given- fx,y=ex-y-ey-x To write the exact differential.

Q: Prove that the function y = ecos* satisfies the differential equation: y" + sin(x) y' +y cosx = 0

A: Find y' , y" and put into given differentiatial equation.

Q: Verify that y(x)=exsinx is a solution to the differential equation   2ycotx-d2y/dx2=0

A: Consider the given solution to the D.E. Differentiate it w.r.t x twice to get the double derivative…

Q: • Determine the value of C for the given first order differential dy y(lny-Inx+1) equation dx when…

A: To find:- particular solution of given differential equation

Q: Find the total differential. w = e3y cos(5x) + z5 ||

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Q: 1. Find the total differential of the ff. at (1, -2).

A: The given function is f(x,y)=xy2-3y+2

Q: What is the linear differential equation of dy/dx+2xy+xy^4=0 using dv/dx?

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Q: Obtain the differential equation of all straight lines at a fixed distance p from the origin * O…

A: The general form of equation of a line which is at a constant distance c from the origin is…

Q: of the differential equati

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Q: Find the general solution to the differential equatio y" + 4y = cos 2x (where y' = ) dx

A: When the right-hand side of a higher-order linear differential equation contains a function of the…

Q: Form a differential equation by eliminating arbitrary Function. Z= (x + y)f(x² + y² ) %3D

A: Given z = (x+y)f(x2+y2)zx+y = f(x2+y2)                             (1) Partially differentiate with…

Q: Consider the differential equation x¨(t) + x(t) = 5t2 − 2 cos 2t.  Write down the ansatz for xp…

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Q: 7. Find the differential dy for y = x2 – 4x + 6, then evaluate it when x = 2 and dx = 0.1 -

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

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

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Q: Find the general solution of the differential equa- tion / - a?y = -x - xy, %3D where |r| < 1.

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Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relatio y…

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Q: c) Show that y, = x* – x² Inx over the interval (0, 0) is the particular solution to the…

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Q: find the third-order differentials z=e^x * cos y

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Q: Use integration to find a general solution of the differential equation                  dy /dx = x…

A: Given: dydx=x1+x2 Multiply both sides by dx dy=x1+x2dx

Q: Compute the differential dz of the function. z = a°!l 9,,11 dz

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Q: Estimate Ay using differentials for the given function and the given values of a and dr 2/3 y =xe-,…

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Q: Find the differential equation by eliminating arbitrary constants "A" and "B" from the family of…

A: Formation of differential equation: As a rule, one requires n+1 relations to eliminate n quantities.…

Q: Find the differential equation by eliminating arbitrary constants "A" and "B" from the family of…

A: The given family of curves                    y=Acos12x+Bsin12x , where A and B are constants.

Q: Consider a differential equaUion -x2 y' = xy + xe

A: we have been given a differential equation with initial condition y(0)=0 y'=xy+xe-x2

Q: Find the number N such that the differential (y^3-2x)dx+Nxy^2dy is exact

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Q: Consider the nonhomogeneous differential equa 1 "(x) + y(x) = e '+ sin a

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Q: 1 Solve for the differential of y when y=sinzx, x=÷, and dx= - 3 A) B) 2 -- C) D)

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Q: Find the function y: (0.x) → R that satisfies the ordinary differential equation ry'(x) + y(x) = x²…

A: Given : y : 0 , ∞→ℝ   ;  xy'(x)+y(x)=x2 cosx        ;  yπ = 0 To Find : solution of ordinary…

Q: Find the general solution of the differential equation y + wóy = cos ot, w² w%. Use C1, C2, C3,...…

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Q: Evaluate the curve f(x, y) = 0 which passes through the point (0,4) and satisfies the differential…

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Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

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Q: Find the 5th order differential of the function y=xcosx.

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Q: Find the second order differential of the function y=e2u, where u=u(x).

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Q: Find the second order differential of the function y=u3, where u=u(x).

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