(b) Solve the initial-boundary value problem Vi – Vzz = 0, v(0, t) = v(1,t) = 0, t> 0, v(x, 0) = 1 – 4(x), 0 0, %3D

Q: Find the critical points of ƒ(x,y) = (x³y-y³) 5

A: To determine the critical points.

Q: Solve the inhomogeneous 1st order equation Ux − Ut = cost U(x, 0) = 0.

A:

Q: Given g(x,y) = 6x^2 - 2x^3 + 3y^2 + 6xy. Find the 2 critical points.

A:

Q: g(y) y - 1 y²y + 1 2

A: to find critical points of gy=y-1y2-y+1

Q: 4) (e* + y)dx+ (2y + x)dy = 0 %3D

A: Hence, the general solution is                                            y=-x±x2-4(ex-C)2 Where C…

Q: + x + + 3y where x(0) = 0 and y(0) = 0. ||||

A:

Q: Metodo de coeficientes indeterminados 3y´´-2y´-y=x^2+3x-6     y(0)=0    y´(0)=0

A:

Q: 2. Find the local maximum and minimum values and saddle points (if any) of the function f(x, y) = xy…

A: Here, the given function is: f(x,y)=xy-2x-2y-x2-y2

Q: If ƒ(x) = f (t³ + 5t² + 7) dt then ƒ"(x): =

A:

Q: If f(x) = S5 (t³ + 7t² + 3) dt then f"(2) =O

A: To find the second order derivative , we first invoke the fundamental theorem of calculus , which…

Q: (x-2)²(x³-4) y = Vx2+1 dy If then equals to : dx O y [2/(x-2)+(3x^2)/(x^3-4)-2x/(3x^2+3)] O…

A: The formulas which are used to solve the above problem are stated with the solution.

Q: Q1// Use Tow Phase method to solve the Mathematical model * (Stop at Table 1 in Stage Two) MinZ=x,-2…

A: Given -  Min Z = x1 - 2x2S.T :x1 + x2 ≥ 2-x1 + x2 ≥ 1           x2 ≤ 3x1, x2       ≥ 0 To find - Use…

Q: Integrate (a) S2(* dt (b) S(x+1)³ dx (c) cos(-x)(x²)dx

A:

Q: If F()dt= x*, then f(8) = %3D (A) 32 (B) 0

A: Given: By Euler's formula for integral,              ddx∫0x3f(t)dt=ddx(x4)⇒f(x3)…

Q: 1. (10 points) Use the method of variation of parameters to solve y" + 4y' + 4y = e-2t In t

A:

Q: Exercise 2. Solve the optimal тахи (t) Sit. 3 control problem [( 1-2x² (4) +2^²^(()) + x' (t) = 4…

A: Given ∫031-2x2t+2u2tdt  Such that x't=4 ut, x0=1 Use the given information solve the integral.

Q: Q1// Use Tow Phase method to solve the Mathematical model * (Stop at Table 1 in Stage Two) MinZ=x,-2…

A:

Q: 4. Consider a fish population in a lake. Suppose some toxic substance flows into the lake so that…

A: Please see the answer below

Q: The population of a community is known to increase at a rate proportional to the number of people…

A:

Q: How do I use the Bernoulli sub for the eq:   (  x^2 ) (dx/dt)= x^2t+3x^3 and where x( 0) =2 thanks…

A:

Q: Consider the IVP dy = (). Iy(20 -- y), y(0) = 1. dt %3D (a) Solve the IVP, finding y explicitly as a…

A:

Q: DE dx dt = x² - 4x + 3. (a) Its stable critical point is X = unstable critical point is X =

A:

Q: Find and classify all the critical points of f(x, y) = x³ - y³ - 8xy.

A:

Q: solve  utt- 4uxx=x2          -infinity 0  subject to initial conditions: u(x,0) = x  ut(x,0)=0

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.