4. If a lion lies stretched out over the entire length of the branch in question 3, exerting a constant force of F = 500 N/m over the entire length of the 1.5 m branch. It is given that I = 1 × 10¬º m* and E = 2x 10° Nm-. The boundary conditions are y(0) = 0, y'(0) = 0 , y''(0) = M and y''(0) = –2M. Use your notes to model the fourth order differential equation suited to this application. Present you differential equation with y'''' subject of the equation. Use direct integration and solve this equation in terms of M. Determine the deflection (in terms of M) at x = 1.5 m. Do not use Matlab as its solution will not be identifiable in the solution entry. You must indicate in your solution:

Q: 7. Points X and Y lie on WZ and Find WY. WX 2 WY 7. ==, and XZ = 37.5 centimeters. XZ YZ

A:

Q: 1. Find the length of the curve given by e' (sin t+cos t) , yY = e'(cos t – sin t), x = 1<t< 4 .

A: The length of a parametric curve is given by L=∫abx't2+y't2dt Now, we have…

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A: The solution is given as

Q: 4) S(x, y) = (4x-x* )cos(y) on the Ans. Absolute max.: 4 at(2,0) 3/2 Absolute min.: at 2 rectangular…

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A:

Q: Given r"(t) = (e^t, sint, cost),  r(0) = (1, 0, 1),  r'(0) = (0, 2, 2),  solve for r(t).

A:

Q: The tangent line to y = f(x) at (1,—8) passes through the point (9,-7). Compute the following. a.)…

A: We can solve this as follows:

Q: Let F(x) = f(x°) and G(x) = (f(x))* . You also know that a° = 14, f(a) = 2, f'(a) = 3, f'(a") = 6…

A:

Q: 2. Find L .2 t2 sin(2@t) F(t) = А. %3D 20 sin(@³r) F(t) = В. 2ot t sin(@t) С. F(t) =- %3D 20 cos(@t)…

A: The given function is Fs=ss2+ω22 We have to find the inverse Laplace transform of F(s). To find this…

Q: Find the equation of the parabola whose axis is vertical and passes through (-1,0), (5,0) and (1,8).

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A:

Q: If z = x2 + y?, x = e' cos(s) and y = e' sin(s), then %3D dz at (t, s) = (1,0) is as %3D

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A:

Q: If xy + e' = e, find the value of y" at the point where x = 0.

A:

Q: Determine the sequence of the generating function A(8) = – log. (1 – s)\s |

A:

Q: 5. For ø = z sech¯³[y tan¬²(In x)], find the directional derivative when dx = 2dy = –3dz at a point…

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Q: 6) Let x = t2 + 4t , y = 2 - t, for -4 <t < 1. (a) Eliminate the parameter and write the equation in…

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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.