Find the solution y(t) to the following 3x3 system with given initial condition y(0) = (2, –2, 1)': 3 y' -1 У (Hint: Use rational zero theorem to find integer roots of the characteristic polynomial)

Q: Show that the following functions are harmonic in x and y: log√x² + y²

A: Solution

Q: Can you answer it and explain your steps

A: Step 1:   Step 2: Step 3: Step 4:

Q: Find an equation for the linear function which has f(0.5) = 0.8 and f(0.8) = -0.3

A: to find linear function which has f0.5=0.8 and f0.8=-0.3

Q: B Electrical condenser An electrical condenser with initial charge Q, is allowed to discharge.…

A: Given equation is: Q=Q0ekt We have to solve this equation for t.

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A: This is linear equation so we can use Lagrange auxiliary equation to solve this problem.

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A:

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A: Here s(t)=t6-3t2+5 We have to find the acceleration at t=1.

Q: Solve the ff. ( Inspection )

A:

Q: Find the x and y coordinates of all inflection points. f(x)=x³ +45x2

A: given function

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A:

Q: 5x°+7x Differentiate f(x) - using quotient rule. %3D 2x2-4x+5

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Q: x+2 Determine the (x,y) location of the hole for f(x)=- x² - 4

A: Holes occur when a duplicate factor is cancelled in the numerator/denominator of f(x).

Q: x2 – x - f(x) = х2 — 5х Determine the point of intersection with the abscissa axis and with the…

A: We can solve the problem by finding the intercept of the function respect to the axis.

Q: A particle moves according to the equation: v(t) = evt – 1 Solve for the unknown(s). V. s t, s v(t),…

A: According to the question:   A particle is moving along the equation, where v(t) is defined as:…

Q: all work to get credit. All parts (5)/(x+3)=(x-1)/(4)

A:

Q: хр %3D S + X хр Find at (-7, 1) if xy: %3D (Rou

A: We have to find dy/dx   at (-7, 1)

Q: The traffic flow rate (cars per hour) across an intersection is r(t) = 400 + 1000t 180t2, where t is…

A:

Q: Write a in the form a = a-T + an N at t-0 for R(t) = t²i+

A: Given Rt¯=t2i+t+13t2j+t−13t2k We have to write a in the form a=aTT+aNN Since, Rt¯=t2,t+13t2,t−13t2…

Q: The windchill index announced during the winter by the weather bureau measures how cold it "feels"…

A:

Q: Ex.: Solve dx dy 2- dt -x- e' dt dy dt dx +2. +y%3Dt.. dt versity-Civil Enginee & Num. A

A:

Q: Evalut the experessions x+3 and 2x when x is 4

A:

Q: d2y at the point (2,) 48. Given yax-i.find -1, find - at the point|2, ах x

A: Given:The function y2x2 = 1.The point (2,1/2).

Q: Question in photo

A: given:

Q: Solve the equation using Bisection method ( 5 iteration) (1,2) F(x)= x3+4x2-10

A:

Q: If ƒ(2)=z²+1 then u(x,y) = 3+y² 3- y² + 1 83+y²-1 3- y²

A: Given  f(z) = z2+1 We know that z = x+iy Hence f = (x+iy)2+1 = x2+2ixy+i2y2+1= x2+2ixy-y2+1

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.