1. Problem 1. Solution to the initial value problem Sy" + 2y + y = 8(t – 2) l y(0) = }, y(0) = 1 function y(t) is differentiable at time moment t =2." (T/F)

Q: Using y' = 6 - m = f' 1 = 6 Step 3 5 2 1 5 ,x-1/2 -1/2, we can now find the slope of the tangent…

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Q: If y(w) = V8 + x°dx then y'(w) = %3D Calculator > Next Question

A: the objective is to find y'(w)

Q: 6. (1 + x)y' + y = √x

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Q: · Sº t³ dt then f'(x)= If f(x) = and f'(-2) =

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Q: (xii) f(t) = 3e'cosh4t (xiii) f(t) = 3e-2"(sinh2t – 2cosh2t)

A: Given :-  The table of Laplace transforms below and any relevant properties used. (xii) f t = 3 et…

Q: If f'(x) = x - 2x-x +2, thenf has a relative minimum at x= -2 O0 0 O0

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Q: 21) y" – 2y' +10y = 0, y(0) = 3, y'(0) = 3.

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Q: (a) Determine all critical points of the given system of equations. (b) Find the corresponding…

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Q: 4 - Let y = f(x) = (a) Find f-'(y). (b) Solve the equations f(x) = a for a = –1,0, 0.5, 2, 3.7, T,…

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Q: If f(x) = X = x-9 x+3' where is f not differentiable?

A: Important point regarding rational function:-If function is a rational function then it is…

Q: Polynomial Function Leading Coefficient Degree y-intercept X-intercepts Sketch of the graph 1. y…

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Q: xy' + ()y = x - 1 (2x+ х+1

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Q: dy when x = 3 ? dx 14. If f is a differentiable function and y = sin what is (A) cos(f'(9)) (B)…

A: Explanation of the answer is as follows

Q: tS W C (b) Suppose that a function h is such that h(-1) 5 and h'(x) 2x +3. Find the equation of the…

A: The derivative of the function h(x) is given by,

Q: 19) y"- 4y'+5y= 0, y(0) = 1, y'(0) = 2.

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Q: Can you give the interval of the solution as a Bernoulli Equation?  y(0)=1 ie...  y'+p(x)y=g(x)y^n…

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Q: 5y" – 28y' + 15y = 0, y(0) = - 4, y'(0) = - 24.4 y(t) =|

A: The given differential equation is 5y"-28y'+15y=0 ........ i,  y0=-4,  y'0=-24.4 The expression for…

Q: - Differentiate the function (find F'(x)) if F(x) = sin(t² + 1) dt

A: Apply Leibnize's. Rule

Q: 2. If y = x +3x-2x+1, find the values of the following e. derivative, i. У"(2) d'y ii. dx ii. y" (2)

A: Please refer to the image below

Q: Q9// find the general solution (sec'x + (cotx)y)dx + (Insinx)dy = 0

A: Using the basic properties of trigonometry and expanding the expression we can find the solution to…

Q: Y"'-3y"+3y'-y=0  y(0)=1 y'(0)=0 y"(0)=0

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Q: find y(t) 2.) y" + 7y' +12y = 16e^2t + t ; y(0)=6, y'(0) = 4

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Q: Q3/ Find f'(x) = y' 1. y = (2vx-4)5 2. y = (x+2)2 3. f(x) = x43 2 ++3

A: Use the power law of derivative and chain rule of derivative.

Q: y''' — 4y'' + 13y' + 50y y(0) = 4, y'(0) = 10, y’’(0) = 42 y(t) = = 0

A: Given: Differential Equation: y'''-4y''+13y'+50y=0 Initial conditions: y0=4, y'0=10, y''0=42 To…

Q: If y" = 1 (x + 1)² y(0)=2 y'(0) = 1 then y'= and y=

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Q: Fnd the solution to the initial value problem: dy/dt = (2t)/(y+t^(y)), y(0) = -2

A: Here the question should be , dy/dt=(2t)/(y+(t^2)y ) , y(0)=-2. I have solved it accordingly .…

Q: 5' + 8 ? 2' +9 What is the long-run behavior of the function y = As t → -0, y Edit As t → 0, y →…

A: To find:

Q: The population of a town grows at a rate proportional to the population present at time t. The…

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Q: y" + 4y = 0, y(0) = 1, y'(0) = - 1

A: Given that: y''+4y=0,y0=1,y'0=-1

Q: If f(x) is a twice differentiable function with f(0) = 3, f(2) = 3, f' (2) = 4, Then æ f" (x)dæ =

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Q: y'' + ly = 0, yl - 4, y' s'(=) - 2 y(t) =

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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.