Verify that any function of the form Y(t) = c1vi + czt* satisfies the equation t*Y"(t) – ĮtY"(t) + 2Y (t) = 0. Determine the solution of the equation with the boundary conditions Y(1) = 1, Y(4) = 2.

Q: Eliminate the constant: 2x 3x =c₂₁e²x + c₁₂e³x Oy"-y'-6y=0 Oy"-5y'+6y=0 Oy"+y'-6y=0 Oy"+ 5y'+6y=0

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Q: If y = Vx? – 2x then y' 2(x-1) 3x2-2x %3D

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Q: Verify whether yı = 3t4 and y2 = 4 t-2 form a fundamental set of solutions for f y" +7t y' + 8 y =…

A: We will verify the given statement.

Q: Find the gradient of the function and the maximum value of the directional derivative at the point…

A: The given function is g(x,y)=lnx2+y23 We have to find the gradient of the function and maximum value…

Q: The equation of then tangent line to y?e2* = 3y + x2 at (0,3) is y= – 6x + 3 A) True B) False

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Q: 2. Find the local maximum and minimum values and saddle points (if any) of the function f(x, y) = xy…

A: Here, the given function is: f(x,y)=xy-2x-2y-x2-y2

Q: d'y (3x-5)(2x + +9x=6) Determine the and of y = 7x Solution:

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Q: Find y as a function of t if 16y" + 16y + 4y = 0, and y(1) = 2, y'(1) = 3. y =

A: The given differential equation  and the initial conditions .The objective is to find the solution…

Q: Use variation of parameters to find the particular solution to 3t y'' + 5y + 4y = 2e Y(t)=| Preview

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Q: Find the maximum and minimum of f(x,y) = yx2 + y(y - 1)2 subject to x2 + y2 =1.

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Q: Find the extreme values ​​of f(x, y) = 2xy subject to the condition x + y = 2.

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Q: Find y as a function of t if y(0)= 4, y'′(0) = 1. y(t) = 25y" + 30y' +45y = 0,

A: given

Q: Parameterize x(y) = √√y+5y using y = t Ans=

A: The parameterization of x(y)  using  y = t  is  x(t)=t​+5tExplanation:Given expression is…

Q: (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

A: Let us find the four second partial derivatives of the given function in the next steps.

Q: State the maximum interval over which the solution  is valid.

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Q: Approximate y(0.8) in the function y' = x - 2y when y(0) = 0, x(0) = 0 and the stepsize is 0.2 using…

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Q: Let A, B and C be sets. It is given that AUC= BUC and AnC= BnC. Shơw that A = B.

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Q: 4. Find and classify the stationary points of each of the following functions: (a) f(x, y) = x³ +…

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Q: For y(t) solution of y'=-4y(1-y/4)+3 find the intervals where the function of t is increasing or…

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Q: Verify that y = x² – 1 is a solution of (y')* + y² = -1. %3D

A: Given;            y=x2-1 is a solution of y'4+y2=-1 We compute the first derivative.…

Q: Fill in the blank The equilibrium solution(s) of y' = 3y(1–where k > 0 are %3D he difference y',…

A: Equilibrium solutions for a differential equation are given by  y'=0 Also wronskian of two solutions…

Q: Find the maximum and minimum values of h(x, y) = xye 2-y4 2

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Q: The vibrating system governed by + x + x = 0 has an initial position x(0) = 4 velocity (0) = 0.…

A: with initial positions and initial velocity

Q: Eliminate the constant: 3x =c₁e²x + c₁₂e ³x Oy"-y'-6y=0 Oy"-5y'+6y=0 Oy"+y'-6y=0 Oy"+ 5y'+6y=0

A: Application of differential equations

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.