What values of α and A make y=Acos(αt) a solution to y′′+6y=0 such that y′(1)=2?

Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A: Sol:- A second order linear, homogeneous ODE has the form of   y''+py'+qy=0y'' -6y' +9y=0Here…

Q: The indicated function y, (x) is a solution of the given differential equation. Use reduction of…

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

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Q: 4. (15pts) Identify (write down) the type of DE, and find the general solution. (y – 3x)dy = (x +…

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Q: 1. Given the initial values are xo =2 and x, =3, find the solution x3 for f(x)=x -6 by using %3D %3D…

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Q: Find a general solution to the given Cauchy-Euler equation for t> 0. By"(1) – 3ty'(t) + 4y(t) = 0…

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Q: 2. [1+ytan(xy)]+ |+xtan(xy)y'=0 (DE with IC

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Q: 3. General solution of (ylny - e-xy)dx + ( + xlny) dy = = 0

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Q: what value of n can be used to transform the Bernoulli equation y'+p(x)y=q(x)y^n into an equation of…

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A: The indicated function y1x is a solution of the given differential equation.By using the reduction…

Q: 2. The boundary-value problem y" = y +2y+ cos x, 0sxs y(0) = -0.3, y() =-0.1 has the solution y(x) =…

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Q: 1) Using Modified Euler's method, solve y'= xy2 + y given yo) = 1 if h= 0.1 to obtain y(0.1), y(0.2)…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: y" + 3y' + 2y = cos(e).

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Q: . Find the general solution to y + 2x = 5y³. dy . Solve the initial value problem of (sin x) = y cos…

A: Topic:- differential equations Note :- as per our guideline if more than one question uploaded than…

Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

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Q: 1 Obtain a numerical solution of y-1 = using Euler's method with step size equal to (0.02) y and…

A: Given 1yy'-1=x3y

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A: Given 16y''-40y'+25y=0

Q: Find the general solution of (3xy-y²)dx-(x²-xy)dy=0

A: As the equation is homogeneous , put y=vx and solve .

Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

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Q: 1 Find the complete solution of y" - 2y' + 2y =x + e* cos x.

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Q: 19. Find the particular solution to y' = 2sin(x) given the general solution is y = C-2cos(x) and the…

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Q: 8.Using variation of parameters, solve for the particular solution of : (D² – 3D+ 2)y = cos (e¯*) O…

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Q: he method used in solving the first order Bernoulli's equation +b(x) y=c(x) y where n#0, n#1 is…

A: Bernauli equation substitution

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: The indicated function y, (x) is a solution of the given differential equation. Use reduction of…

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Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

A: Explanation of the answer is as follows

Q: 8. The auxiliary roots of the auxiliary equation associated with a certain homogeneous LDE are m =…

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Q: The indicated function y, (x) is a solution of the given differential equation. Use reduction of…

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Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

A: Given: Differential equation x2y''-xy'+17y=0 and its first solution y1 = xcos4lnx. To find: Second…

Q: e general solution to the DE  is(6x+y2)dx+y(2x-3y)dy

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Q: The indicated function y, (x) is a solution of the given differential equation. Use reduction of…

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A: The differential equation is 36y''-60y'+25y=0 and one solution: y1=e5x6. We need to calculate y2…

Q: solve the problem by method of characteristics  y du/dx -4xdu/dy = zero  where the initial…

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

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Q: The indicated function y1 (x) is a solution of the given differential equation. Use reduction of…

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Q: The indicated function y,(x) is a solution of the given differential equation. Use reduction of…

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Q: 1) Using Modified Euler's method, solve y' = xy² + y given Y(0) = 1 if h= 0.1 to obtain y(0.1) ,…

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Q: The indicated function y1(x) is a solution of the given differential equation. Use reduction of…

A: Given: Differential Equation36y''-60y'+25y=0y1=e5x/6 To Find: use…

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: 2. Using the method of undetermined coefficients, find a particular solution of V +y =t(1+ sin t).

A: we have to find the general solution of y''+y=t(1+sint)

Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

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Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: 2. Find the solution of the given initial value problem using Method of Undetermined Coefficient…

A: As per Bartleby guidelines we're supported to answer only first one question when two or more…

Q: Using the variation of parameters method to find a particular solution of a nonhomogeneous DE with 3…

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Q: Find a solution for y' = y - y, y(0) = 0.2, h = 0.1 %3D using Modified Euler's Method. Hint: do 5…

A: Given that, y'=y-y2, y0=0.2, h=0.1

Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

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Q: 1) Using Modified Euler's method, solve y' xy2 +y given yo) 1 if h=0.1 to obtain y(o.1) Y(0.2) %3D

A: According to our Company Guideline we must do only one question in case more than one question is…

Q: 3. Find the general solution of the Bernoulli's Equation. y = 5.4y – 12y, y(0) = 1. %3D

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Q: The indicated function y, (x) is a solution of the given differential equation. Use reduction of…

A: Given that the function y1=x sin(5ln(x)) is a solution of the given differential equation…

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.