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: 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: 3y = /2y – 1, y(1) = 1. ) Find the solution y = y(x) of this IVP. Please present your solution y =…

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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: At every point of the graph of the function y=f(x) we have y″=12x and at the point (0,5) the tangent…

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Q: Find the linear approximation to f(x)=x2+1x−2 near a=3.

A: Given: f(x) = x2 +1x − 2; a = 3

Q: P(t)y'' + Q(t)y' + R(t)y = S(t) is this a linear equation?

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Q: Find y as a function of if y(0) = 18, y'(0) = 28, y'(0) = 21. y(x) = y"-9y" + 20y = 24e,

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Q: Find the the stationary points and the local extreme values of the function f(x, y) = −2x/x2 + y2+1

A: The objective is to find the stationary points and the local extreme values for the function…

Q: 3(3y² + x²)dy - 2xydx = 0 when x = 3, y = -2

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Q: 4. Solve x²y" - 5xy' + 8y = 4x², for the boundary conditions y(1) = 1, y'(1) = 1.

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Q: Consider the three basic vectors: (2,1,0,-1),(-1,1,1,1),(2,7,4,1) a. give two vectors that are in…

A: Given the three basic vectors:                           (2,1,0,-1),(-1,1,1,1),and (2,7,4,1) We have…

Q: 1. Describe each of the following equations, giving its order and telling whether it is ordinary or…

A: 1)Given DE is y"+3(y')2+4y=0. We find it's order and decide whether it is ordinary or partial and…

Q: Find y as a function of a if y"" - 12y" + 35y' = 24e", y(0) = 27, y'(0) = 11, y'(0) = 30. y(x) =

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Q: Let y be the solution of the equation y' = 4 - 2xy satisfying the condition y (0) Use Euler's method…

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Q: show that the solution y(t)=e^2tsin(t) is linearly independant.

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Q: Q5. Write the governing equation of 1-D heat transfer with convective heat loss and indicate all the…

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Q: Find the function g(x) satisfying the two conditions: 1. g'(x) =-512x³ 2. The maximum value of g(x)…

A: To find the function  satisfying the following two conditions:(2) The maximum value of  is 5.

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: 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: Determine 4sin(x); the value of the arbitrary constants y(x) = C₁e* + c₂e¯* + y(0) = 1, y'(0) = -1…

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Q: Assume that  dx1/dt= x1(10-2x1-x2) dx2/dt= x2(10-x1-2x2) a) Graph the zero isoclines. b) Show…

A: Given- Assume that  dx1dt = x110 - 2x1 - x2dx2dt = x210 - x1 - 2x2 To find-  Graph the zero…

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: Is the equation y '(t) = 2y - t separable?

A: Given a differential equation, y't=2y-t

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 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: 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

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.