Q3/ Determine the solution of a?u du arz subject to boundary conditions u(0,t)= u(2,t) = 0 %3D at and the initial condition u(x,0) = x, where 2 is the length of the bar.

Q: Let W(x) = W[y,, y2, Y3] , where 11 V1, Y2, Y3} are solutions to y"+3x y' -4y 0. Then W" =3 W.…

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Q: Find the general solution.

A: As per guidelines ,we will solve only first question.

Q: Solve 1) y" + y = e* + x² 2) y" – y' – 6y = e-2x + 4sinx

A: here first take d/dx = D then make its auxilary equation then find complementary solution then find…

Q: FIND 2 DIFFERENT (LINEARLY IN DE PENDËNT ) SOLUTION S POR THE D.E y"_x² y'- 3 xy = O *y'-3xy%3D0

A: Step:-1 Given that y''-x2y'-3xy=0 ---(1) This is second order differential equation with variable…

Q: Eliminate the constant: y=x+c₁₂e¹+c₁₂e\ 1 Oy"-y=-x Oy"-y'+y=0 Oy"-y'=x Oy"-y=0

A: Given: The given equation y=x+c1ex+c2e-x To find: we need to eliminate the arbitrary constant.

Q: Find the particular solution for (2y3 – x³) dx + 3xy² dy = 0 when x = 1, y = 1

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Q: FIND 2 DIFFERENT (LINEARLY INDE PENDENT) POR THE D.E. SOLUTIONS y"_x² y'- 3xy = o 2.

A: The linear homogeneous ordinary differential equation has the form pxy'' +qxy' +rxy=0. If the…

Q: Given the function f (x, y, z) = ln(x³ + 4y² – z) – x, calculate the partial derivative with respect…

A: Given function - f(x,y,z) = lnx3+4y2-z-xWhile differentiating f(x) with respect to x, then y and z…

Q: 4. Solve x²y" - 5xy' + 8y = 4x², for the boundary conditions y(1) = 1, y'(1) = 1.

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Q: Determine the interval where b must belong so that the function f(x,y)=x^(2)+bxy+y^(2)−b^(2)x−2by…

A: We are given, f(x,y)=x2+bxy+y2-b2y-2by..............(1) and x2+y2<925................(2) We need…

Q: The solution of the IVP y" – 3y' – 4y=0, y(0)=0, y'(0)=5 is: Select one: a. y= -e 4t+ e! b. y = -…

A: Using Method of Laplace Transform to solve IVP

Q: а. у' +3у%38, у(0) %3D4 b. 1 xdx+dy= 0, y(0)=8 y c. senxdx+ ydy=0 y(0)= -2 d. y' +2xy2 = 0, y(0) = 3

A: y = -srqt(2+2cosx) is a solution of:

Q: Let y be the solution of y'+y=x, xER,y(-1)=0. Then, y(1) 류를 ²-28² 2-2e -

A: Since given that y be a solution of differential equation…

Q: 5. Solve the equation SHOW YOUR COMPLETE AND CLEAR SOLUTION. (y')² + (x - 2r ) y' + x- - xt = 0 X -…

A: We will use only the basic knowledge of differential calculus to answer this question properly, in…

Q: Let y1, Y2 be two independent solutions of t?y" – 2y' + (t + 3)y = 0. %3D If w(y1, y2)(2) = 3, then…

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Q: 02/ Solve the system derivative to find the general solution of each (x & y as a funtion of t). dr…

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Q: Using the method of characteristics, find a solution to the partial derivative equation xux + uy = u…

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Q: 2. Find implicit solution x dy y dr x² +1 y² +1'

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Q: 11) If f(x,y) = xe' – y In(x² +1) find af af and dy

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Q: x²y" + xy' – 9y = 48x³ .3 %3D

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Q: b. y"-3y" + 4y = 0, y = 1, y'= -8, y"= -4 when x = 0 %3D c. y"+y"-0, y(0) = 2, y(0) = 1, y"(0) = -1…

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Q: Q1: Find partial derivatives of the function with respect with each variable 4) f(x, y) = Vx² + y²…

A: We find the partial derivatives of the given function f(x, y)=x2+y2, by using the definition of…

Q: a, b, c, d

A: Hello, thanks for the question. Since we only answer up to 3 sub-parts, we’ll answer the first 3.…

Q: x)is solution for x²y"+xy + (2x2- 4)y=0 ylgn İhi

A: True

Q: Use method of characteristics to solve ux+uuy=0 with u(0,y)=2y. What is the domain of validity? Is…

A: Solution to the differential equation

Q: Solve the IVP dy r(x² + 1) 4y3 y(0) dr V2

A: We are given: dydx=xx2+14y3 ⇒4y3dy=x(x2+1)dx Now, Integrating both sides,…

Q: 11. The behavior of the system is a saddle. x' = x + y, y' = −x +y

A: