) Use the d'Alembert solution to solve = 2 -00 < x < o0, t> 0, 1 u(x, 0) = e, u(x, 0) : 1+ x2*

Q: Eliminate the constant: 2x 3x =c₂₁e²x + c₁₂e³x Oy"-y'-6y=0 Oy"-5y'+6y=0 Oy"+y'-6y=0 Oy"+ 5y'+6y=0

A:

Q: Let p and q be the two roots of the equation mx? +x(2-m)+3=0. 2 Let m,, m, be the values of m…

A: Given mx2+x2-m+3=0        ...(i)

Q: Prove that if G is a graph with spanning tree T and e is an edge of G that is not in T, then the…

A: Given that G is the graph with spanning tree T and e is an edge of G that is not in T Let x and y be…

Q: Find an antiderivative F(x) of the function f(x) = 4x² - 6x +5 such that F(1) = 14. F(x)= (Hint:…

A: Solution is given below:

Q: Find an antiderivative F(x) of the function f(x) = - 2x²5x + 2 such that F(0) = - 15. F(x) = Now,…

A: On solving this we will get

Q: Verify whether yı = 3t4 and y2 = 4 t-2 form a fundamental set of solutions for f y" +7t y' + 8 y =…

A: We will verify the given statement.

Q: x3 1+x² dx

A: Note : according to our guidelines I can solve only one question, please reroute the remaining one.

Q: If (1 – i) x + (1 + i) y = 1 - 3i, then (x, y) =

A:

Q: Solve Ux + X YUy +U=0

A:

Q: Determine whether the functions f1(r) = e2*, f2(x) = e-2" , and f3(x) = sinh 2x are linearly…

A: To determine whether the functions f1x=e2x, f2x=e-2x, and f3x=sinh 2x are linearly independent on…

Q: Let A = (²2²) 22 Find et and the general solution to X' = AX + (1)

A:

Q: 7. Find the value of h(2) given that (ho gXx)= 4x +4x+4 and g(x) =2x + 1.

A:

Q: f (x) = { ₂x² (²/²) ² 2=1 Coso f(z) dz= ? 23

A: We have to calculate

Q: Solve the ODE =n, x²y" + xy' −y=_de x+1 -

A:

Q: In(ere + 12) dx Xet

A: Given : ∫x2ex2lnex2+ 12dx

Q: 1 — х x(х + 1)

A: Inequalities

Q: Show that the y = √x/₁/4(kx²/2) is a solution of y" + k²x²y=0_

A:

Q: 5 What is the derivative of5a2 + 10x + ? A None of the given choices B 10x + 10 + 3x2 10a4 + 10a³ –…

A:

Q: 11. Solve x² - x - 2 in Z3[i] = {a + bi : a, b € Z3}.

A: We have to find solution of x2 - x - 2 over Z3[i]. We know that  Z3[i] = { 0, 1, 2 , 1+i , 2 + i ,…

Q: For the difference equation given by y(k + 1) + y(k) = 3 (1/2)* with y(0) = 1 Find the expression of…

A:

Q: Q2: Solve the ODE =n, x²y" + xy' - y = - x+1

A:

Q: b) Solve ди Ət ди +3x = 1+u, Әх -8AHAB, u(x,0) = f(x). t > 0,

A: Given pde is  ∂u∂t+3x∂u∂x=1+u,  -∞&lt;x&lt;∞, t&gt;0 and u(x,0)=f(x) we have to solve this pde

Q: 1 1 .3 x° + 3 1 Given the function f (x) = -x* – x2 a) Determine f'(x). Consider the function f (x)…

A: Dear student. You have posted many questions. According to the policy, we will answering the first…

Q: dN + N = Ntet+2 dt

A: we have to solve first order of differential equation given below

Q: Consider the following functions. (x) = 2 + x, f,(x) = x, f;x) = x² g(x) = c,f,(x) + cof2(x) +…

A: A set of vectors {v1,v2,...,vk } is linearly independent if the vector equation x1v1+x2v2+···+xkvk…

Q: Find the values of the coefficients a, b and c so that the conditions f(0) = 1, f'(0) = -10, and…

A:

Q: -Vx2+5 -x f(x): f'(0)? -x+2

A: