Consider the following initial-value problem (IVP): y"-2y'+5y = 10sin x, y(0) = 2, y'(0) =1 a) By solving the auxiliary equation, find the complementary function, y,-

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A: Solution :-

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Q: b) Use Euler's method to obtain a numerical solution of the differential equation dy y = 4 - dx with…

A: given             y' = 4 - y/x     and y(1) = 3, we have to find

Q: Show that y = sin−1 x satisfies the differential equation y = sec ywith initial condition y(0) = 0.

A: The given differential equation is y' =  sec y,  with initial conditions y(0) = 0.We want to show…

Q: on) solve the Differential en by using vanation of parameters - 24 (+12 yll -24¹ +y₁

A: Please see the below picture for detailed solution.

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Q: 2. Solve the first-order linear differential equatio a. y' + 3y = e3x

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A: Given: x=0 is a regular singular point of differential equation 4xy''+2y'+y=0. To find: Indicial…

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A: here is the solution

Q: 10x – 8yva? +1 fip dx 2 = 0.

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A: see 2nd step

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A: I have given solution in step2

Q: Find the particular solution of the first-order linear differential equation        y′ + y = 6ex…

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A: I am attaching image so that you understand each and every step.

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Q: Solve the differential equation with initial conditions y" - 3y 10y = 4e5t y(0) = 0, y' (0) = 1…

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Q: 1. The order of the differential equation 5x- d'y aty + 3x + w'y = 0 is

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Q: Write down a differential equation of the form = ay+b where all solutions approach y = dt as t → 0.

A: The given question is solved below.

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Q: The Bernoulli's form of the differential equation x³ydx +(3x² - y³)dy=0 is

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A: Given- yy'-2ex=0 To find-  The particular solution of the above differential equation  that…

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Q: Consider the autonomous first-order differential equation dy/dx = y - y and the initial condition…

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Q: Suppose the motion of a mass-spring system is described by the differential equation x"+By'+1y=0.…

A: We will use knowledge of basic differential calculus to solve this problem.   It should be noted…