6. Solve the Cauchy problem Ut + xux = -tu, u(x,0) = = COS I.

Q: 21. y" - 2y + 5y = e cos(2x).

A: We have used variation parameters method.

Q: 6) Find X 11 df dx by using chain rule if f=u+= cos² u G(x)= U=πX 7) Say whether the function is…

A:

Q: Find and of the implicit equatio: a 3x?z + y – xyz' = 0 b ye-* + z sin x = 0,

A:

Q: Suppose that 3x² - y² = t² and y=tsin 0. Find (27). = sin e 0 X = 0 and

A: Given 3x2-y2=t2 and y=tsinθ

Q: 9. y = C,eax cos(bx) + C2eax sin(bx); a and b are parameters

A: As per our guideline we are supposed to answer only first asked  question. Kindly repost other…

Q: 31, 32, 33, and 34 Find y" by implicit differentiation 31. 9a22 9

A: Refer to the question , we have to find the y” by the implicit differentiation as,

Q: 12. Find the second derivative for the function f (x)=4x+12x²-20x-18 and solve the equation f"(x)=0.…

A:

Q: 12) Use Newton's Method to find the closest root to xo =1 for f(x)=x-In(x+4)

A: Given: Function f(x)=x-ln(x+4) and x0=1To find: use newton method to find the root near to x0=1

Q: 3. 2√3 sin 2x = -√3, [0, 2π)

A:

Q: Use undetermined coefficients or annihilator y" + 25y = 6 sin 5x + x² %3D

A: To find the general solution of the given differential equation.

Q: 35) y = -4 sin x 4+ 2+ 2n -2+ -4-

A: