Show that the differential equation x³y² + x(1+yº)y' = 0 is not exact, but becomes exact when multiplied by the integrating factor 1 μ(x, y) = Then solve the equation. xy? The given equation is not exact, because My = 726 y which is different from N=1+y6 After multiplication with u(x, y), the equation is exact, because then My = Nx = 0 The general solution of the differential equation is given implicitly by 1 =c, for any constant c, where y > 0. y6 + 6 ln(y)

Q: ll is thrown vertically upward from the top of a building (when t-Oseconds). It has a height functi…

A: Topic:- application of derivatives

Q: The function f(x) = = The smaller one is x = 2x³36x² + 192x - 1 has two critical numbers. and the…

A: The given function fx=2x3-36x2+192x-1

Q: Which equation of a circle has the center, C, and radius, r, as shown in the graph? -3-2 7 T of 7 T…

A: The circle has center C3,-2 and radius 26

Q: DETAILS ZILLDIFFEQMODAP11 4.1.002. The given family of functions is the general solution of the…

A:

Q: Find V (V x F), if F(x, y, z) = 6ei +9rej - 7ek. V. (V x F) =

A: To find ∇·∇×F, if Fx, y, z=6exz i+9xey j-7eyz k.

Q: Set up a double integral that gives the area of the surface of the graph region R. ƒ (x, y) = xª –…

A: Topic:- application of derivatives and integration

Q: Let f(t) be the weight (in grams) of a solid sitting in a beaker of water. Suppose that the solid…

A:

Q: The function f(x)=x^{2/3} does not satisfy the conditions of the Mean Value Theorem on [-8,8]…

A: To find out the correct option.

Q: On (-∞, ∞), three functions y₁(x) = cos 2x, y2(x) = sin² x, y3(x) = cos²x are linearly independent…

A:

Q: Let y = 2√x. Find the change in y, Ay when x - 2 and Ax - 0.3

A:

Q: Given the graph of f' below, which of the following is (are) true about f at x=a? (a) f is…

A:

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: The given function is: fx=x9-9x  Analyze and sketch a graph of the function. Find any intercept,…

Q: Let y 3x². Find the change in y, Ay when x = = 4 and Ax = : 0.2 Comm Find the differential dy when x…

A: We have to solve given Questions.

Q: II. Consider the function f(x, y) defined for all (x, y) by ƒ(x, y) = 232/32 + 2xy + 4x²y (a) Find…

A: Here we have to find the critical points.

Q: Find curl (82 i + 9x j + 6y k). curl (82 i + 9x j + 6y k) = = ( )k )i + (i )j + (

A: To Find : curl(8z i + 9x j +6y k)

Q: Question Use an appropriate linear approximation to estimate √48.95. (Round your answer to three…

A: Given data÷ Use linear approximation to estimate 48.95 Since 49=7 is easy to compute and 49 is close…

Q: Evaluate the following integral. Sx² e 19x dx --- 2 Let u=x. Use the integration by parts formula to…

A:

Q: Find an approximation of the area of the region R under the graph of the function f on the interval…

A:

Q: Sketch a graph of the polar equation. 3 2+3 cos 0

A: The given polar curve r=32cosθ

Q: Calculate the indicated Riemann sum Sn​, for the function ​f(x)=x2−9x−4. Partition [1,7] into six…

A:

Q: Let f(x)=√x - 5. f(3 + h) – f(3) h Then lim h→0 If the limit does not exist enter DNE.

A:

Q: Solve the initial value problem y" — 2y' — 35y = 0, y(0) = a, y′(0) = −15. Find a so that the…

A:

Q: Question Find the linear approximation L(x) of the function f(x) (Enter an exact answer.) Provide…

A:

Q: A moon's elliptical orbit around a planet is modeled by the equation 225x² +576y² = 176,400, where…

A:

Q: Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then…

A: We need to find Laplace transform.

Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

A:

Q: The volume of a right circular cone of radius x and height y is given by V volume of the cone is 247…

A: To find dydx

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: Given function is x9 - 9x

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y - 5xyz + 10yz²…

A:

Q: Identify this surface, φ = π/3 in spherical coordinates, and find its equation in x, y, z…

A: Identify this surface, φ = π/3 in spherical coordinates, and find its equation in x, y, z…

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. the…

A:

Q: Find the following values. Round answers to 3 decimal places as needed. csc(-13°)~ sec(5)≈ tan( -8)…

A: Basic trigonometric transformations are required

Q: 4. Which of the following is the vector projection of (1,0, 1) onto (-2, 4, 0)? 2 B. (-1,2,0) c.…

A:

Q: and a "0" to be false. P 1 1 1 1 0 0 0 0 q 1 1 0 0 1 1 0 Write a truth table for the proposition:…

A:

Q: sider the following function. y = 6x In(x) y'(x). () = dy"(x). x) =

A:

Q: 13. +27x-27 √x² dx √x² - 6x +9 2 (Ans: x³ + x² + 36x + 81ln|x − 3| + C)

A:

Q: At time t = 0, a bacterial culture weighs 4 grams. Three hours later, the culture weighs 8 grams.…

A:

Q: Match the vector field with its graph. F(x, y) = xi + 3yj mammon M T Pinnal bandill SEREN C -9 in C…

A:

Q: Find the particular solution of the differential equation that satisfies the initial condition.…

A: We have to find solution of the given initial value problem.

Q: Consider the following. Find its foci. Find an equation of the ellipse. smaller x-value 2 larger…

A:

Q: 3. Find the value of (T) for a solution (x) to the initial value problem: y" + 25y = 10 cos 5x; y(0)…

A:

Q: Your answer is correct. Find a differential equation whose general solution is = = C₁e⁹t + c₂e-³t.

A:

Q: Solve the system using Cramer's Rule. 2x + 5y = -25 -x+3y=-4 Find the determinant D (denominator).…

A: Please refer to the image below

Q: Use the formula k(t) k(t) = TEREST {|r' (t) × r"(t)|| ¡|r' (t)||³ r(t) = esti + e-tj to find (t).

A: The given curve rt=e5ti+e-tj

Q: An infinite series [x_n converges if the sequence (S_n) of partial sums given by S_n=x_1+x_2+...+x_n…

A:

Q: Evaluate I C: arc on y = x³/2 from (0, 0) to (4, 8) (2x −y) dx + (x + 3y) dy.

A:

Q: c) Write the polar equation for a conic section with eccentricity 3, a focus at the pole, and a…

A:

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: Solution of given question is written in below steps.

Q: -4 -2 ora y 8 6 4 2 -2 f(x) = |x| 2 4

A:

Q: Lucas is walking on a circular path modeled by the equation (x+6)² + (y-2)² = 36, and Neal is…

A: