,Analyze the stability of equilibrium, and make a rough sketch of the solution, y(f). Hint: start by finding the first term in the Taylor series of the velocity field, but don't use direct differentiation! - In(1-sin' y) (cos(sin' y)-1) di y(0) = 0.1

Q: 16. F(m, r) = Gm/r² at (100, 10)

A: We wil use rules related to multi variable calculus to solve this.

Q: 4) f(x) = | -1<x<1 Ans. 25

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

Q: Use forward and backward difference approximations of O(h), and a centered difference approximation…

A: Given function is, fx=sinx1+cos Then the forward Oh is,…

Q: Solve the ODE  y'+(1/x)y-ex=0, when x>0

A:

Q: 14x10 14x10 - 2100f 1. The velocity of a rocket is given by v(t) = 2000 ln -9.8t,0<t<30 where v is…

A:

Q: ind the slope of the line that is tangent the curve sin(2x)+sin y=e*y – 1 at (0,0). our answer…

A:

Q: Q3: Find the first derivative of y= cos(x) at x= t/2 using a step size of h= Tt/12. Use forward and…

A:

Q: Find the directions in which the function f(x, y) = x²y+exy sin(y) Increase and decrease most…

A:

Q: Use a linear approximation (or differentials) to estimate the given number to the nearest hundredth.…

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Q: d mula sinh (t) = In (t + VE? + 1) and- (In(t)) = } %3D ne derivative of sinh(t).

A: Here we use rule of differenciation to find the required derivative.

Q: V(1) (1) 20 10 + 0 -10 -2t 1 N 3 4 v(1) 5 10 7 t(s)

A:

Q: ) Find the first derivative: b) y = log7 v1+x

A:

Q: By differentiation with respect to time, show that the equation x = xi + ut + 1/2 at² describes…

A: Given that, x=xi+ut+12at2. Where, xi is the initial position. u is the initial speed a is the…

Q: 6. Find the derivative of y = t2 ? = 2t b) = 2t d) = 2 a) 2 dt 4..

A:

Q: Let y(t) be the height (in meters) after time t (in seconds) of a rover that is landing on some…

A:

Q: 1)™ Determine a formula for the derivative of (x° + that works for any integer m. m y'

A:

Q: Let y(t) be the height (in meters) after time t (in seconds) of a rover that is landing on some…

A:

Q: In (2x) ty= S sin (3e') dt. fy D

A: Given fy=∫0ln2xsin3etdt

Q: Compute the second derivative with respect to r of 3x + 8 y = at x = 1.

A:

Q: Let y(t) be the height (in meters) after time t (in seconds) of a rover that is landing on some…

A:

Q: Find the derivative, or y', of ³ – Vy = ¿y² + 6 at (2,1).

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.