(i) ae2* + 2xe²* = 8e2« (ii) e2 – 6e" – 16 = 0 (iii) In z+ In(r – 3) = In(5x – 7)

Q: 2. Use Euler method to compute ys for the DE yy'=2x for y(1)=3

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Q: 1.Solve the partial differential equation -7 = 0, by method of separation of variables ây

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Q: 2 What is the solution of the initial – value problem d²y =X O with y(0) = 1 dx? and y'(0) = -2 ? у…

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Q: The solution of the differential equation (xy – y²)dx – (x² +y²)dy = 0 is : A) 2 In + 1|- tn -;…

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Q: (b) Obtain the general solution of y^ prime prime +2y^ prime +y=e^ -x ln x on (0, ∞)

A: To find- Obtain the general solution of y'' + 2y' + y = e-xlnx on 0, ∞.

Q: 2.(Trivial) Verify that for any positive integer n the piecewise defined function x2n+1. – x2n+1. x…

A: y = x2n+1, x<0andy'=(2n+1)x2n+1-1y'=(2n+1)x2nVerifying;xy'-(2n+1)y=0L.H.S.=x (2n+1) x2n -(2n+1)…

Q: 2. Find the particular solution to y " = sin(x) given the general solution y = -sin(x) + Ax + B and…

A: The general solution to the differential equation y''=sinx is y=-sinx+Ax+B

Q: Using the operators obtained above, obtain the differential equations provided by only the functions…

A: Given : u'(x)+v'(x)-2u(x)-v(x)=0-2u'(x)-v'(x)+u(x)=0

Q: Solve the diffevential cauationm. du e cosn=0,0 X2015,40)-a. Alam - Moislton method with h=0.4.

A: The given differential equation is, dydx+y-e-xcosx=0

Q: 2. Find the particular solution of sin y(x+sin y) dx +2x² cos ydy = 0 :3(-1) = 2

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Q: The partial differential equation is to solve: XUx + YUy = 0, with U(0,Y)=e-y^2  and i have that the…

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Q: 8. A weight of mass 8 kg is suspended by a spring with k = 10 N/ m and c = 1.6 N s/m. The initial…

A: Given, Mass m=8 kg,Spring constant k=10 N/m,Damping coefficient c=1.6 Ns/m,External force…

Q: Find infinite power series solutions for the differential equation. (x³ + 1)y" + x^y=0

A: The power series solution of a differential equation mostly involves when the coefficients are in…

Q: Here are three second-order differential equations with initial conditions: c) x(t): - 3x + 2x = Zet…

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Q: 2. Find the general solution of (2x-3y-2) dx-(x-2y)dy = 0

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Q: Find a series solution about the ordinary point 0 of the differential equation y" +8xy-4y= 0 O None…

A: To obtain the power series solution of the second order differential equation, use the following…

Q: 5. Obtain the particular solution. y'"-2 y'+2 y=3e" cos 2x; when x 0, y=2,y'=3

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Q: Find the largest interval in which the solution of the initial value problem y" + csc(t) y' +…

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Q: 4. Find infinite power series solutions about x = 0 for the differential equation: (x² – 1)y/" +2xy'…

A: We will find out the required solution.

Q: If y = f(x) is a function satisfies the differential equation f'(x)x³ + f(x)3x² = x³ ,where C…

A: We have to solve the given differential equation and find f(x).

Q: 1. The following table shows the number of absences and grades of 2 students in a Differential…

A: The objective is to compute r i.e correlation coefficient and to determine grades in differential…

Q: 2. A company has contracted to manufacture 10,000 closed wooden crates having dimensions 3 m, 4 m,…

A:

Q: 5- in the differential equation en x = 0 is a) Normal point the ation the x*(x − 3) ý + (3x +2)ý+x*…

A: Given : A differential equation x3(x-3)y''+(3x+2)y'+x4y=0 To find :  If for x=0 then it is a (a)…

Q: Solve the problem := (1+ 4x)/y over the interval from from x = 0 to x = 1 using a step size of 0.25…

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Q: The solution to the initial value problem y" + y = 8 cos 2x – 4 sin x, y () = -1,y () = 0 is y = -n…

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Q: Soru 2) x(x - 2)y"- (x2-2)y' +2(x- 1)y 3x2 (x - 2)2 e* Obtain the general solution of the…

A: Given - xx-2y'' - x2 -2y' + 2x-1y = 3x2x-2ex To find - The general solution of the differential…

Q: 2. Find the particular solution of (3sin y- 5x) dx+2x cot ydy = 0 ;y(-1)=-

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Q: 6. Show that y(x) = Inx is a solution of xy" +y' = 0 on interval (0, 00) but is not a solution on…

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Q: 4) One of the solution of the equation y"(x) + p(x)y' (x) + q(x)y(x) = 0 is given by yı (x) =…

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Q: 2) Show that y =1 - Ce-* is a solution of the differential equation = 1- y for any real number C. dx…

A: Our guidelines we are supposed to answer only one question. Kindly repost other question as the next…

Q: 1. Show the drawing and entire solutions to know the differential equations of the lines' families…

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: 6. Find two power series solutions of the differential equation about the ordinary point x = 0: y" +…

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Q: 2y – x = 3t y + x' = 3e-t ¤ (0) = y (0) = 0 3(s-1) L (x) s2(s+1)(2s²+1) 3(2s-s-1) s2 (s+1)(2s²+1) L…

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Q: 4) Let y(x) be the solution of the initial -value problem y' = cos(x + y), y(0) = 0. Use Euler's…

A: To find the solution of initial value problem.

Q: 7. Obtain the particular Solution by satisfying the conditions indicated. 3x dy; when x = 2, y = -1.

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Q: 4. Find a particular solution of y" + y' = cost cos 2t cos 3t.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: y" - 5y'=x-2, when x = 0, y = 0, y = 2

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Q: y'+ytan(x)=cos^2(x) ,      y(0)=-1

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Q: Compute the general solution valid near the origin ((+4x² )y" - By = O 'y= s{1 - 4x°) + a»\x=…

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Q: ... Find the general solution of the system of linear differential equations (expr83s your answer in…

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Q: Obtain a numerical solution of 2y + y - x=0 using Euler's method with step size equal to (0.5) and…

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Q: 3 9 dx dt -1 -3 with x(0) 4 Give your solution in real form. X1 = X2 = ||

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Q: What are the Mixture Problems? How these are related with differential Equations?

A: Mixing Problems:  If we will start with a substance that is dissolved in a liquid. Liquid will be…

Q: 7. Use the Fourth Order Runge-Kutta method to solve y'-y = 0, y(0) = 1 on the interval 0, - v with h…

A: The formula for the fourth order Runge-Kutta method is dydx=f(x,y) with the initial condition x0, y0…

Q: 2) Suppose you have a differential equation that satisfies the conditions of Theorem 6.2.1-…

A: We find first three non zero terms by using initial conditions and given recurrence relation.

Q: (12) Show that the Initial Value Problem S lu(x)| = 1 rE (-1,1) u(x) = 0 r= -1,1 has no (classical)…

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Q: In the Four-Step Rule, which among the steps is the most important, upon which the foundation of…

A: We need to eliminate ∆x from the denominator else the limit does not exist.

Q: Le(3 sinh 2t-5 cosh 2t) = 1+5s A. s S>1 +2s -3 1+5s В. s2 ' +2s +5>1 1-5s С. s+2s+5 s>1 1-5s D. s² +…

A: From the table of Laplace transformation, it can be written that:…

Q: If Newton's method is used to find the critical number of f(x) = a® – a³ + æ² – 2x with initial…

A: Image is attached with detailed solution.

Q: 4. By using differential method solve 1 1 1 th + + + n terms ...... 1.4.7 4.7.10 7.10.13

A: The solution of this question is given below: