Find the curvative for y = 2t" at t = 1. (Use symbolic notation and fractions where needed.) K(1) =

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A: Solution:- Correct option :- a Detailed explanation

Q: (x2 – 1)y" – 2xy' + 2y = 0 - tion ofS the o uation

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Q: Consider the equation E : y² = x° + 8. Compute 2P and 4P for P = (1,3).

A: Given clear explanation below

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Q: lif the solution of the following initial value problem is y(x), find y(6)]. S 6xy' – 6y = 7x, ly(1)…

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Q: 5) Find the general solution by using reduction of order method to t?y" – ty' – 3y = 0 given that…

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Q: A series RL circuit with R = 50 2 and L = 10 H has a constant voltage V = 100 V applied at t = 0 by…

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Q: Consider the following IVP: y"-3y'+2y = e*; y(0) = 0, y'(0) = 0 Find the general solution.

A: We solve the given DE  y"-3y'+2y=e3t.......(1) y(0)=y'(0)=0......(2)

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Q: 1. The number of bacteria in thousands in a refrigerated food is given by N(t) = 20t – 20t + 120 for…

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Q: y(3) for y' = xe3x - 2y, y(0) = 0 by using Euller's method. h = 0.5

A: Here I write a small piece of python code to solve this problem.

Q: Consider the following IVP: y"- y = 4cos t; y(0) = 0, y'(0) = 1   Find the general solution.

A: The given differential equation is: y''-y=4cost So, we can also write as: D2-1y=4cost So, the…

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Q: Let y(x) be the solution for the DE : y = (x + y + 2)2 If y(0) = -2, then find y() ○2-푸 O 8 - T O -…

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Q: Find a general solution to the following ODE. -3t y" + y' – 6y = e¯

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Q: Let z=xIn(x²+y²-e)-235xy, x=te, y=est. If the value of oz when s=2 and t=1 is equal to Ae?+Be", then…

A: Here, the given functions are: z=x lnx2+y2-e4-235xy, x=t es, y=est so, z is a function of x and y…

Q: Q2. If the solution of the below first order D.E is y = C ef(x,y) (x³ + xy²)y' = y3 Find the f(x,y).

A: x3+xy2y' = y3dydx=y3x3+xy2 ........................equation(1)Let put y = vx in equation(1) and…

Q: 8. Find the solution x (t) of the IVP given as 2" + 4a' + 13x = f (t) x (0) = 0 and a' (0) = 0 }

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Q: 3.Eliminate the arbitrary constant on the given equation: xsiny – x²y-3 = C

A: In this question we have to eliminate the arbitrary constant on the given equation.

Q: Find y' to 3 |х — 1 O y = In x2 O x² In V3x + 5

A: Here we use logarithmic properties ln(mn) =n(ln(m)) ln(m/n)=ln(m)-ln(n)

Q: Q2. If the solution of the below first order D.E is y = C ef(x.y) (x³ + xy²)y' = y3 Find the f(x,…

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Q: What is the general solution of the following ODE * (x² + xy - y²) dx + (1²/7 -(x² - 2xy) dy = 0

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Q: Solve the following O.D.E: (x2 + y?) ý = xy with the initial condition y(1) = 2, on the interval I =…

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Q: Q:2: a) Find implicitly, if y²cosy +x² = 2xy

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Q: What is the general solution of the following ODE* 3 points (x² + xy – y*)dx + (;x² – 2xy) dy = 0

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Q: Q2. If the solution of the below first order D.E is y = C el(x.y) (x³ + xy²)y = y³ Find the f(x, y).

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Q: For ſ k*e3* dx = 1 (ke)3x 3 (1–In 2-1) + C. If u = 3x, then k =?

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Q: Q2: find the general solution: (D* - DD')z = (x² – 2y)e" + sin (2x – y) •2

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A: We use the method of variation of parameters to find the particular solution to the given…

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A: Given data is : f-1=0.5 To draw the particular solution for y=fx

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A: Bernoulli's equation is a special type of first-order linear ordinary differential equation. When…

Q: 2. and XR %3D C. Two tails with n = 34 , x =

A: Solution: From the given information, level of significance is 0.01 and n=34.

Q: dy Solve the initial value problem 4t + 9t2, y(1) = 2. dt (Use symbolic notation and fractions where…

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Q: For x=e2 y=In 2t. find y' when x=e. O 4e e 4e O e -|

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Q: 3. Derive the reductive formula for S sec" (x) dx.

A: We will find out the required solution.

Q: A second solution y2 for the DE x²y" – 4xy' + 6y = 0, can be obtained by reduction of order with the…

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Q: Find the general solution to the 2nd order ODE: y" + 4y' + 4y = √xe -2x

A: To find the general solution to the given 2nd order ODE.y''+4y'+4y=xe-2x

Q: Find the general solution of the given ODE: dy x²y-4y dx x+2

A: The solution of the given differential equation is  y=e(x22-2x+C)or y=Ce(x22-2x)

Q: Find the curvative for y = 4t" at t = 1. (Use symbolic notation and fractions where needed.) K(1) =

A: Please see the explanation below

Q: pitcher of buttermilk initially at 25°C is to be cooled by settling in on a place where the…

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Q: Ex: Find the solution of The e ditt evential equation xy? with yCi) =1 2xy 2 dy

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Q: The ODE ty" – 2ty' + 2y = t has a particular solution Yp(t)

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Q: y(5) + 9y' = 0

A: The given differential equation, y5+9y'=0 is a homogeneous linear differential equation with…

Q: Find the general solution of the ODE. y" + 4y' + 4y = x-?e-2* on (0, 0)

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Q: a x In the experiment of tussing a fair coin is the randam variable giving 3 times the number of…

A: Given three fair coins are tossed. So PX = 0 = 18P(X = 1) = 38P(X = 2) = 38P(X = 3) = 18

Q: Consider the following IVP: y"-3y'+2y = e3t; y(0) = 0, y'(0) = 0 Find the general solution. y(1) =…

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Q: (1+ 4.x²)y" – 8y = 0 equation xo = 0 1

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Q: Q2. If the solution of the below first order D.E is y = C ef(xy) (x³ + xy2)y' y3 Find the f(x,y).

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Q: eAt = I + At + A²2 + + 2! k! k=0 o compute eAt and e-At (; ) 1 A = 0 2 eAt = e-At Need Help? Read It

A: Given, eAt=I+At+A2t22+...+Aktkk!=∑k=0∞Aktkk! A=1002A2=10021002=120022⋮Ak=1002⋯1002=1k002k