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

Q: provide

A:

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

A: We have used variation parameters method.

Q: If the following eq. is exact, then solve it (y cos x + 2xe) + (sin x + x²e + 2)y' 0.

A:

Q: (sinx)" dx is:- 4) The solution of (sin x) dx A) (sinx)' dx B) C) Zero

A: ∫0πsinx7dx=∫0πsin7xdxWe know…

Q: +(1+3) sin.xdy = 0 34. cos x dx + 1 +

A:

Q: 4x x*e*dx (2sin dx V4-x2

A: We can solve all the intregration problems with tha mathod of substitution. In substitution we use a…

Q: 14. Solve: (xux + yu, = 2u lu(x, 1) = cos(x)

A:

Q: 5) By false position method the equation f(x) = e- 3x has a root between 0.5 and 1.0.

A: This question is about regula falsi 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: Solve the differential equatons (7x-ty +16) dy + (2x-5y+12) dx=o when x-3, y= 2

A:

Q: If x'y" + xy'+(x? -y=0 x>0 ,y,=x 2sinx , and y=y,v. Which of the following %3D equations satisfied…

A: Let   y1 and y2be two solutions of the second-order linear differential equation d2ydx2+Pxdydx+Qxy=R…

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: Solve the following equations y" - 4y + 4y = 8x² + 4x y" - 2y - 3y = sin 2x

A:

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: 29. Solve (x3 + y³)dy+ x²y dx = 0. %3|

A: Given problem:- Solve (x3+y3) dy +x2 y dx=0

Q: B. Find f(x) if f

A: Solution of the problem as follows

Q: I. Functions and Limits 1) If f(x) = x2 – x + 3, find f(-5y) and f(x³) x2-1 2) lim X-1 2+3x-4 3) lim…

A:

Q: 1 0 5) Solve the equation x'=| 2 1 -2 ). x X 13 2 1

A: The given problem is to find the solution for the given matrix differential equation.

Q: 9.) y(4) + 2y" +y = x² sinx

A:

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

A:

Q: ry"+xy'+(x* -y =0 -)y = y = x cosx is a solution of the equation Show that

A: Given               x2y''+xy'+(x2-14)y=0                      (1)

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: 3) Solve S(4cos? x+4 sin? x)dx

A: Given:

Q: 7. y = tan e³x + etan3x

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: S cos 4x cos 3x dx

A: Given: I=∫cos(4x)cos(3x)dx

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

A: