5.32. z = sin(x² + y?)

Q: What is N(x,y) for the following differential equation: x(1 – sin y)y' = (cos x – cos y – y) %3D

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Q: 9. Find the differential of f(x) = e* at 1 with increment of 0.2. A. 0.2e B. e0.2 С. е D. 0.1e E.…

A: Given query is to find the differential of f(x) using increment.

Q: For what value of k is the following differential equation exact? (3r² – kr²y + 2) + (đ² – 4x² +3) -

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Q: cos x dx + (1 + sin x dy = 0

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Q: Consider the following linear differential equation x dy/dx + 2y = sin(x). a) Calculate the…

A: The objective of the question is determine the I.F. and solution of the differential equation.

Q: 6. Find the total differential for the following equation of the following equation; z = ex² + y²…

A: We Know that  For function z = f(x, y) whose partial derivatives exists and  Total Differential of z…

Q: xdy – ydx = (x² + xy – 2y²)dx %3D |

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Q: (v – cos "x)dx + cos x dy = 0

A: The given differential equation is: (y-cos2x)dx+cos x dy=0 Rewrite the equation as: (y-cos2x)cos…

Q: Find the Total Differential of each of the following functions. 12. x2 + y? 13. (x² – y?) 14. sin-…

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Q: b) Given the following differential equation Diberi persamaan pembezaan berikut dy x- = 3y+x dx…

A: Given differential equation is                       x dy/dx =3y+x

Q: (a) Find the differential dy. y = V 15 + x² %D

A: y = f(x)dydx = f'(x)dy = f'(x) dxy=15+x2dydx = ddx(15+x2)dydx = 1215+x2 ddx(15+x2) dydx =…

Q: (a) For what values of k does the function y = cos(kt) satisfy the differential equation 100y 49y?…

A: Given y=cos(kt) satisfy the differential equation 100y"=-49y

Q: nd the differential equation of a family of circles, each having its center on the line y = x and…

A: We have to find the differential equation of the family of circles from given data.

Q: 1.find the differential of the following functions

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Q: The following Differential Equation is exact. Use the fact that M(x,y)=F(x,y) and N(x,y)=F(x,y) in…

A: The following Differential Equation is exact.  Use the fact that M(x,y)=F(x,y) and N(x,y)=F(x,y) in…

Q: Salve the following differential equation using Frobenius methad 2x(1-x) dy +3y=0

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Q: The instructions are to show that the following relation defines an implicit solution of the given…

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Q: Solve the following differential equation using appropriate method. 3. (r+ sine - cose) dr + r(sine+…

A: r+sinθ-cosθdr+rsinθ+cosθdθ=0

Q: 4. x dx + (x²y + 4y)dy = 0; y(4) = 0

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Q: y3 sin 2x dx - 3y2 cos? x dy = 0 %3D

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Q: ... Solve the following differential equation using the indicated method. (b) y" +4y= sin 2x using…

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Q: Consider the following differential equation f + = cos (x) What is the general solution ?

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Q: en the following differential equation: y" + 4y tan? 2x Using the method of variation of parameters,…

A: given differential equation is y''+4y=tan22xFind out the proposed particular solution of the given…

Q: (b) Solve the following ordinary differential equation using Runge-Kutta classical method. Compute…

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Q: Find the differential equations for each family of curves under the following conditions: a, b)…

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Q: 6. Determine the differential of each of the following: 1.y= 3e* +3 tan(2x)

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Q: g8 The lartial differential equation d'u 3Q4is %3D Claddlificd as:- fa) larakolic (6) sliptic (d)…

A: Consider the equation of the type: Rr+Ss+Tt+f(x,y,z, p,q)=0 where  r=∂2z∂x2 , s=∂2z∂x∂y, t=∂2z∂y2,…

Q: tind the particular solution of the differential (0?+ 4D +3)x given that t- 0, and dx -2 %3D

A: Given differential equation is : D2+4D+3x=e-3t At t=0, x=12 Att=0 ,dxdt=-2

Q: 5. Circles with center on the y-axis

A: A point on y -axis is always of form 0,a where a∈ℝThen circles with center on y -axis and radius…

Q: Solve the following differential equation, (s x)+(cos x) y = 3 sin x with the initi al dx condition…

A: Given differential equation is (sin x)dydx + (cos x)y = 3sin x

Q: ind the differential equation of the family of curves described in the following 1. Straight Ines…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: What is N(x,y) for the following differential equation: x(1 - sin y)y' %3D (сos x - сos y — y)

A: Given a differential equation, x1-sinyy'=cosx-cosy-y

Q: Find the differential equations of the following primitives by eliminating the arbitrary constants.…

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Q: y' = xcosecr + y cot r.

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Q: C. Evaluate the following exact differential equations 2. (e* siny + tan y)dx + (e* cosy + xsec?y)dy…

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Q: a sin a + In v ) da + tan adv = 0 COs a

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Q: Ive the following differential equation using the indicated method. y" +4y= sin 2x using Method of…

A: Given y"+4y=sin2x

Q: The following differential equation (+1)² + ² = sin a dy dx x has an order of 0 0 O 3 O 1 02

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Q: Given the differential equation (2r cosx – 1)r'=r?sin x, obtain the value of U = M dx A U=-r-sin x…

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Q: 24 ue'sin(s + 2t)

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Q: y (x² + y² – 1)dx + x(x² + y² + 1)dy = 0 %3D

A: Given the differential equation y is not exact.

Q: (2) Find the differential of each of the following functions. In other words, for each of the…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) √ dy y = 2√x +

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Q: 1. Solve for the differential of the following given the values of the variables and their…

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Q: Identify the differential equation of the following: (2a? - r2) dr = r³sine de; when 0 = 0, r = a

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Q: Find the solution to the following differential equation. Take the constants of integration to be…

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Q: Find the approximate value of the following by use of differentials. 1. √626

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: y(x + y)dx + (x + 2y – 1)dy = 0 (determination of integrating factor) %3D

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Q: (b) Solve the following ordinary differential equation using Runge-Kutta classical method. Compute…

A: The differential equation