Q5. Write the governing equation of 1-D heat transfer with convective heat loss and indicate all the parameters involved in it.

Q: 5. Solve the diffusion equation = v dt drr dr

A: ∂θ∂t=v∂2θ∂r2+1r∂θ∂r such that- r=0, θ is finite, t>0r=a, θ=0,         t>0 and θ=P4μa2-r2

Q: Q1: Find partial derivatives of the function with respect with each variable 3) f(x, y) = (xy –1}…

A: Solution

Q: A heat-seeking particle is located at the point (2, 3) on a flat metal plate whose temperature at a…

A:

Q: 2. Draw a phase line for the equation y' = y (y – 5). If y(0) 2, what is the lim y(x)?

A:

Q: z = x3 – xy? + 3y2

A: Let us consider the two variable function z=f(x,y) The first partial derivative of the function is…

Q: dz at the point (1,1,1) if the equation 4xy +z°x-2yz = 3 defines z as a function of the two…

A:

Q: Solve the two-dimensional heat conduction equation д2z 22z 1 дz dy²k ət + = dx² by the method of…

A:

Q: Differentiate implicitly to find the first partial derivatives of w. x2 + y2 + z2-9yw + 10w2 5 aw…

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Q: . Form the differential of the system of circles touching the y-axis at the origin.

A: The solution is given as

Q: Find both first partial derivatives. h(x, y) = e-(x$ + y5)

A:

Q: Q1: Find partial derivatives of the function with respect with each variable 1) f(x, y)=2x² − 3y – 4…

A: Solution

Q: Find all the second partial derivatives of 3 (x,y) = 4r°y– 7xy?

A:

Q: Q1: Find partial derivatives of the function with respect with each variable 1) f(x,y)=2x² – 3y – 4…

A:

Q: z = x3 – xy? + 3y² |

A:

Q: 5xy = 4x?z – 3yz?; yx and yz. -

A:

Q: Find the orthogonal trajectories of the curve x^(2) + y^(2) = c^(2)

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Q: Ва ut = Zuxx – ucot )=32 т и (ч, t ) = 52 та heat equation Ic = 4 (xio)= 5x+2 осхи

A: Using separation of variables method

Q: Q4: A vertical steel plate of dimensions 3cm x 3cmamd negligible thickness is in steady state…

A:

Q: Differentiate implicitly to find the first partial derivatives of w                           x2 +…

A:

Q: Find all equilibria of the continuous-time dynamical system given by i = cos x, x e R. Sketch the…

A: Given: Let's find all of the equilibria of the continuous-time dynamical system x˙=cosx, x∈ℝ.Draw…

Q: Find four second partial derivatives. z = e" sin(y)

A: Consider the function z=exsiny Here, the objective is to find the four second partial derivatives…

Q: y' = y– y³e=2x у — узе-2х

A:

Q: 5. Given that 5x623 W = The value of x, y and z are measured with maximum percentage error of 1%, 2%…

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Q: Q2 Find the second partial derivatives of |(x, y) r cos y +y e*

A: Formula: Second Partial derivitave of f(x,y) fxx, fxy, fyx ,fyy.

Q: What is the stability of equilibrium points of A and B? Is the energy of B higher than A?

A: If the vector field lines converge to the point or stay close to a point at all times the point of…

Q: 3- If the value of elasticity is equal to Ey = 0.21 then the ., note that 11.5 = xi = 10, yi %3D…

A:

Q: 6. State whether the equation is ordinary or partial, linear or nonlinear, and give its order. (x +…

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Q: Q2. Find the second order partial derivative of x² - y² + 2xz - xy + yz.

A:

Q: y² + y²eG)° + 2x²•G° x': 2xye 6) Zaye*

A: The solution is given as

Q: B. Find the indicated partial derivatives: af af 7. fls.y) = cn{«-y?), y

A:

Q: 9. If f(x, y) = +, then find the first and second order partial derivatives.

A: Since you are asking multiple questions. As per our guidelines, we are supposed to answer only one…

Q: Given the Ideal Gas Law: P = 10T/V where P is pressure, V is volume, and T is temperature. Find the…

A:

Q: Use​ Euler's method with step size h​ = 0.2 to determine value of y.

A: To determine value of y at x=0.1 by solving the differential equation dydx=y−x1+x,y0=1, and h=0.2

Q: Q4: Solve the one – dimensional heat equation: du ax² 2 where c2-1, to determine the resulting…

A:

Q: Find the partial derivative. 3p f (p, q) = e af

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Q: 1 V.= 6 - |(10cos2t)dt - · | (0.5t)dt mv 0.2 |

A:

Q: What do you mean by asymptotically stable for autonomous equations ?

A: Given: asymptotically stale for autonomous equation A critical point x∘ of an autonomous system is…

Q: Differentiate implicitly to find the first partial derivatives of w. x2 + y2 + z2 - 1yw + 8w2 = 6…

A: let f(x,y,z,w) = x2 + y2 + z2 - 1yw + 8w2 - 6 =0then fx(x,y,z,w) = 2xfy(x,y,z,w) = 2y-wfz(x,y,z,w) =…

Q: (c) Suppose that two of the pipes become blocked so that x3 = 0 and x1 = 0. Determine the flow rates…

A: Topic - flow diagram

Q: Find both first partial derivatives. h(x, y) = e−(x2+y2)

A: The given function is hx,y=e-x2+y2. To find the partial derivatives. Solution: The given function is…

Q: Q1: Find partial derivatives of the function with respect with each variable 2) f(x, y) = (x² –1)y +…

A: To find the partial derivatives of the given function with respect to each variable

Q: Consider a competitive market in which price adjusts to excess demand or supply and firms enter and…

A: given that                                                 dpdt=0.5qD-qs where qD is demand…

Q: xy" – 2y' +=y = 7x5 Given that y, = x² and y2 = x are 2 Linearly independent soluti homogenous…

A: Introduction: The formula for the particular solution by variation of the parameter is given by,…

Q: The standard equation of one dimensional heat equation is a'u ôu d'u ô'u d) a) b) a c) a?

A: One dimensional heat equation: Let u(x, t) denote the temperature at point x at time t. The equation…

Q: obtain a slope field, and add to it graphs of thesolution curves passing through the given points.…

A: We have to find the slope field and add to it graphs of the solution curves passing through the…

Q: How to solve this equation y'''-4y''+2y'-8y=6e^(x) - x^(2) + 1 using Laplace Tranformation. Initial…

A: Consider the given initial value problem as y'''-4y''+2y'-8y=6ex-x2+1 with y0=y'0=y''0=0. Apply…

Q: 1. Identify whether the equation is ordinary or partial, linear or nonlinear and state the order and…

A: Order of a differential equation is given by the highest order derivative present in it. While…