X = A'+(A+B) с х A B 0 0 1 1 1 1 1 1 1 1 1 1 1 x = (AB)'(AC) А в с х A 1 1 1 1 1 1 1 1 1 1

Q: Classify the following system of first-order partial differential equations (k=const.): aw ди aw + v…

A: Consider the following system of first order partial differential equations with k =constant

Q: Verify that 1 $(x, y, z) = satis fies the partial differential equation x² + y² +z? = 0 ax2 ay2 "…

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Q: b) Use Laplace transform to solve the system of differential equations dr 4y, dt dy dt +x = y + 3e*,…

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Q: d.x dy 2- + +x+5у 3 4t, dt dt dx dy dt + + 2x + 2y = 2, dt — 3, у(0) — — 4.

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Q: dæ + 5x + 6 æ dt 4t where: a(0) =2 dt %3D

A: Given dxdt+5x+6∫0txdt=4t where x(0) = 2  x'+5x+6∫0txdt=4t  x(0) = 2  denote x=ϕt…

Q: Solve 3rd order ODE with forward and backward eulers method. from t = 0 to 0.1, h = 0.1, y0) = y(0)…

A: The third order equation is d3ydt3-2y=0. Consider dydt=p, d2ydt2=q⇒p'=q, q'=2y By Forward Euler…

Q: Given a derivative transform of s³Y (s) – s²y (0) – sy (0) – y" (0) – 382Y (s)- 3sy (0) - 3y (0) +Y…

A: We will use the formulae of Laplace transform of derivatives of a function.

Q: What is the differential equation of the orthogonal trajectories of the family of curves x2 - 3xy-…

A: Given family of Curve is x2-3xy-2y2=C

Q: Show that the set of solutions of a second-order linear homogeneous differential equation is…

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Q: Let z = cosh t. Find the differential dz when t = In 3 and dt = 0.2 O 4/3 O 4/15 O 8/15 O 1/3

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Q: Solve the differential equatons x(2y + In ax) dy + (x+y)dx when x=3 y=Ź y= 2 1.

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Q: B/Verify that u(x, y, z) = Tr + yk 4+z? satisfies the partial differential equation a2u a2u a2u = 0…

A: B.

Q: 11. Show that U(x, y, z) = (x² + y² +z²) satisfies Laplace's partial differential equation + = 0.

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Q: 5. Find the differential equa tion of (x-c.)" †C2Y C3

A: We will eliminate the arbitrary constants. As there are 3 constants so it'll be differentiated…

Q: 3.) Let set S = {x, e*,sin x , cos x} be a solution to a 4th-order homogeneous differential…

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Q: Find the differential dy: y = In(sec² ( 3ª²–20+5 312-2x+5 O (E) None of the choices dy = 2 (x – 1)…

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Q: What is the differential equation of the orthogonal trajectories of x3 = Cy? (1) Зxdx + 2уdy — 0 (2)…

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Q: 2. Using Euler's method with N = 8 and 10. dx/dt = 1 + tsin(tx), x(0) = 0

A: Given dxdt=1+tsintx  and x(0)=0 and N=8, N=10

Q: Solve these second order differential equations by applying the Laplace transform. (iii) y" + 4y =…

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Q: x²y" +xy' – y = T

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Q: Find the solution of the differential equa­tion that satisfies the given boundary condition(s) .  f"…

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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: Solve the partial differential equation: ty yu + 9xey y where u = u(x, y), given -y u (1, y) = 3e +…

A: Given - uxy = yuy + 9x2 exy , uy(1, y) = 3 ey + e-y , u(x, 0) = 3x3 - 6x2 + 1x-2 + e5x To find -…

Q: 1. Find the total differential dw. 2. w = re2u +e-V

A:

Q: {[{ ال 1: تحق ق من دالة التالية تحق ق معادلة لابلاس :س Z = In /x2 + y² اضف ملف ك 3. fxy ل لدالة :…

A: To find  Partial derivatives of the given functions

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: dx dy 2 + + x + 5y = 4t, dt dt dx dy + 2x + 2y = 2, dt dt x(0) = 3, y(0) = -4. +

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Q: (x)1/2sin(y/x)

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Q: 1. Show that u(x,t)= etsin kx satisfies the partial differential equation_u₁ = α² uxx

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Q: Show thatƒ (x, y, z) = x² + y² – 2z2 satisfies the Laplace's partial differential equation.

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Q: Suppose that a body moves through a resisting medium with resistance proportional to its velocity v,…

A: (a)

Q: 1. Know the partial differential (Heat Equation): Ut Uxx х € (0,1) , t> 0 U (0, t) U(1, t) = 0 U (x,…

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Q: Are these equation separable 1.s2+ds/dt = (s+1)/st 2.dr= b(cosx dr+ rsinxdx) 3.y'=ye(x+y)/(x2+2)

A: The objective of the problem is to determine whether the given equations are separable. A…

Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A+…

A: In this question we need to find a derivative of the given equation.

Q: 2(150–x2) 100+r 3x2 100- dt 300–2x2 100+1 3x2 100- dx2 di dx2 (5) (300–2x2)(100–1)–3x½(100+1) %3D dt…

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Q: Is the differential equation (uv+u)du = [(u^2)*(v^2) + u^2 + v^2 + 1]dv separable?

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Q: Find the integral surface passing through the curve 1 T: z = sin y + e' +- x = 0 8 of the partial…

A: In this question, we solve the partial differential equation by using the surface condition.

Q: Determine the largest interval (a, b) for which Theorem 1 from section 6.1 guarantees a u solution…

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Q: Find solution to hon-homo geneous heat problem ut = Uxx + Cos(HX) ; +70 17X70 u(x,o)= f(x); OLX <I…

A: We will use basic knowledge of PDE theory and analysis to answer this question.

Q: 4- dt2 d²y(t) dy(t) + 4 dt + 10y(t) = sin 2t u(t)

A:

Q: 3. Find the solutions for the given linear systems of differential equations using Laplace…

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Q: a) By using convolution theorem, show that 1 1 (sin 3t – 3t cos 3t). 54 L- (s² + 9)² b) Using…

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Q: Compute the differential dz of the function. 6.7 Z = x dz ||

A: Here, to find the differential dz of the function z=x6y7 Note that: dz=zxdx+zydy...(1)

Q: Prove that the general solution of the differential equation √√1+cos(t) d0=(√1 + cos(t) — t sin(t)…

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Q: Derive a differential equation for the orthogonal trajectories of the family of curves xy c %3D

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Q: y" + 6y + 9y = t

A: Given: y"+6y'+9y=t

Q: Verify the function z(x,y)=Vx sin is a solution of the following partial differential equation…

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Q: Prove that the homogeneous integral equation 1 p(x) = 1 f(3x - 2) to(t) dt 0 values and…

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Q: Find a general solution of an inhomogeneous system of linear differential quations by the method of…

A: Consider the given system of equations.