Find all functions that form a fundamental set of solutions for t2y" – 2ty' + 2y = 0. O y(t) = et O y(t) = e2t O y(t) = 2 O y(t) = t2 y(t) = t O y(t) = 1

Q: 1. Find the function y(t) satisfying y' = ev-t(1+t?) sec y with y(0) = 0.

A: Claim: solution for with y(0)=0. Integrating both sides we get, Take u=e-y then du=-e-y  and…

Q: The function y=f(x) satisfies the conditions y(0) = 1 and y'=xy³/4. What is y(1)?

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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: ,2k 101. Let F(x) = 2k . k! k=0 (b) Show that y = F(x) is a solution of y" = xy' + y. y(0) = 1,…

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Q: Find y as a function of a if y(0) = 1, y'(0) = 9, y" (0) = -191. y(r) = j y"-7y" -y + 7y=0,

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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: length, is given by the heat equation, ди 2²u əx² Ət (0 0), here x measures distance along the bar,…

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Q: Verify that y = c is (1+ce') (1– ce') is a solution to y' = + (v² – 1) , where some constant.

A: For verifying given thing, we find solution of given differential equation Now, for finding solution…

Q: The function z(x, y) obeys, = -2e Which of the follow represents a valid first step for finding u(x,…

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Q: Eliminate the constant: 3r y=c₁₂e²²+c₁₂e² Oy"+y'-6y=0 Oy"+ 5y¹+6y=0 Oy"-5y¹+6y=0 Oy"-y'-6y=0

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Q: Find y as a function of a if y(0) = 19, y'(0) = 26, y" (0) = 14. y(x) = y"" - 10y" + 21y' = 48e²,

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Q: Find y as a function of t if y(0) = 8, y'(0) = 3. y = 64y" + 304y +361y = 0,

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Q: Find the function satisfying y' x + 3 and y(0) = 2 ... 2y + 5

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Q: Please find the requested derivative of the following functions. s²-4st+t² = 4, find 25 ds dt - ds…

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Q: Find y as a function of t if y(0) = 2, y'(0) = 5. y(t) = 100y" +9y = 0,

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Q: (b) Sketch the following function. Write down its equation in unit step function and find its…

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

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Q: y (2 xy +1)= xy'

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Q: Find y as a function of t if y(0) = 8, y'(0) = 4. y(t) = 6y" + 33y = 0,

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Q: [v= -y +2x ,x' = 4y + x + t

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Q: Find y as a function of a if y" − 3y" − y + 3y = 0, y(0) = −9, y'(0) = −8, y'(0) = 7. y(x) =

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Q: + 12du = 0, t> 0 with u(x, 0) = f(x), 0 < x < 1. Determine the characteristics and sketch them.…

A: Given: The given partial differential equation 3∂u∂t+t2∂u∂x=0 with  u(x,0)=f(x),0&lt;x&lt;1.

Q: Show all work! Find the maximum, minimum, and saddle point of f(x,y) = cos(x)+ (1/y^2 + 1/x)+1

A: We will use the basic knowledge of 2-variable calculus to answer this question.

Q: Find y as a function of if y(0) = 2, y'(0) = 9, y'(0) = -58. y(x) = y"-4"-y + 4y = 0,

A: We are given the homogeneous differential equation: y"'-4y"-y'+4y=0 and y(0)=2, y'(0)=9,y"(0)= -58.

Q: Suppose the equation y" – 4y' – 5y = f(x) has y= 3x' Find f(x). as a solution. (a)

A: if y(x) is solution given equation then it will satisfy the equation

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.