yV + 2y" + y" = re=*

Q: Solve the initial value problem 2yy' +4=y² + 4x with y(0) = 5.

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Q: Find a solution to the initial value problem, y" + 6x = 0, y(0) = -2, y (0) = -5.

A: y'' +6x=0⇒y'' =-6xIntegrating both sides,⇒y'=-3x2+c1Integrating both sides,⇒y=-x3+c1x+c2 We have…

Q: Find the solution to the initial value problem y' + 2y = te-2", y(1) = 0.

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Q: 3. Solve 2x²y" + xy' − 3y = 0 with the initial condition y(1) = 1 y′(1) = 4

A: This is a Cauchy Euler equation. The equation is solved by a substitution.

Q: Solve the initial-value problem: y" – 2y" + y' = 2 – 24e* + 40e 5x 13 y(0) = y'(0) = y"(0) = a. (i)…

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Q: Solve the initial-value problem. x2y' + 2xy = In(x), y(1) = 5

A: using:- 1. y'+P(x)y=Q(x) then solution is,       y. (IF)= ∫ (IF) Q(x) dx +C ,     where,  IF= e∫…

Q: Solve the initial value problem -4sin(2t – 4), s'(0) = 100, s(0) = 0. %3D %3D dr2

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Q: Example 2: Find the particular solution of (x – y)dx + (3x+y)dy = 0 when x = 2 & y = -1.

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Q: Use the Gauss-Seidel iterative technique to find the 3rd approximate solutions to 2x1 + x2 – 2x3 = 1…

A: we take x1=w, x2=y, x3=z So we need to solve the system  2w+y-2z=12w-3y+z=0w-y+2z=2 Starting with…

Q: 3) Find the particular solution of the DE y" = 12x² if y(0) = 1 and y'(0) = 2.

A: This is a problem related to differential equation. Please follow the procedure given below.

Q: 2. Solve the initial-value problem y"(x)+ 4y'(x) + 6y(x) = x², %3D y(0) = 0, y'(0) = 0. %3D

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Q: Find the solution to the initial value problem y'=x²-, y(2) = 3.

A: Solution of the initial value problem

Q: yp=u1x+u2x-2 is the particular solution proposed for the nonhomogeneous Cauchy-Euler equation…

A: we have given particular solution of the given differential equation.

Q: 4) Find the solution of y'= 2(2xy) passing through (0,1).

A: Given, Equation  y'=2(2x-y) passing through a point (0,1).

Q: Solve the initial value problem Ut + 2ux -3u, u(x,0) = 1/(1+x²), == x € R, t > 0 TER

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Q: How do i get the initial value problem xy’ + 8y = x^6 and y( 1) = 5.

A: Given,                   xy'+8y=x6                    ...(1) and                         y(1)=5.

Q: 13.Obtain the general solution of y²dx+x(x +y)dy = 0

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Q: 2. Solve the initial value problem y"+2y'-5y = 4e* -1, y(0) =1, y'(0) =1

A: For the given initial value problem, first find complementary function (CF)  then find particular…

Q: Solve the initial value problem. where A = 1.5 -2 -8 2 -2 x' = Ax, x(0) =

A: Given : x'=Ax, x0=-21.5 where A=-2-82-2 To find : solution of the initial value problem.

Q: Solve the initial-value problem. x²y' + 2xy = In(x), y(1) = 5 %3D

A: givenx2y,+2xy=ln(x), y(1)=5y,+2xy=ln(x)x2this is a standard form of linear diffrenetial…

Q: Find the solution to the initial-value problem. Y = 2xy(1 - 9y), Y(0) = -1 y =

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 3. Find the particular solution of the linear equation dy + -y = dr 1. if y(1) = 0.

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Q: Solve the initial value problem y"+2y'-5y = 4e¯2* -1 y(0) = 1, y'(0) =1

A: First solve the given differential problem and the apply the initial Condition:   The given equation…

Q: 6. Find the general solution of Utt2uxt3uxx = 0 and then find the solution of the initial-value…

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Q: Find the unique solution of the second-order initial value problem. y" - 6y' + 5y = 0, y(0) = - 7,…

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Q: 3) Use the Method of Undetermined Coefficients to solve the Initial Value Problem. y) – 2y" + y =…

A: Given differential equation we have to find the solution for given differential equation

Q: (b) Show that y = 3e²x + e-2x - 3x is the unique solution of the initial value problem y" - 4y =…

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Q: Solve the initial-value problem y"+5y'+6y=0, y(1)=2, y'(1) = 3

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Q: Solve the Initial-Value Problem y' – ty = 0 , y(0) = 1 using any method that we had covered. Please…

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Q: Solve the initial-value problem -2 x' = -1 х, 1 -2 x(0) 3

A: Given information: x' =-201-2x  and x0=-13 Calculate the initial value.

Q: 2). Solve the initial value problem x2= vx-4, x22, y(2) = 0.

A: From the given problem: xdydx=x2-4 So, we can also write as: dy=x2-4xdx∫dy=∫x2-4xdxy=∫x2-4xdx+C...1…

Q: ) Solve the initial value problem y" + 4y' + 4y = 8xe-2 where y(0) = 1 and y'(0) = -2.

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Q: Solve the given initial-value problem. -2 2 X'= × - (- ~~ ) x + (²) X 3 4 2 X(t) 2t 6e-6e²t - 6 X =…

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Q: Solve y' = 6x, x' = x + y with initial conditions x(0) = 1, y(0) = -2.

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Q: Find the solution of (1 + e²)yy = eª that passes through (0, 1).

A: (1+ex)yy'=ex(1+ex)ydydx=exseparation of variablesydy=ex1+exdxIntegrating both…

Q: Find the unique solution of the second-order initial value problem. y" + y' - 6y = 0, y(0) = 5,…

A: y''+y'-6y=0(D2+D-6)y=0D2+D-6=0D2+3D-2D-6=0D(D+3)-2(D+3)=0(D-2)(D+3)=0hence the roots areD=2,-3

Q: Find the unique solution of the second-order initial value problem. y" -y' - 2y = 0, y(0) = – 1,…

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Q: - EXAMPLE 3 Find the particular solution of 3xy' y = lnx + 1, satisfying y(1) = -2. x > 0,

A: It is a first order differential equation.

Q: Find the unique solution of the second-order initial value problem. y" + 16y = 0, y(0) = 2, y'(0) =…

A: Given  differential equation is y"+16y=0, where y0=2 and y'0=-2. Given differential equation is…

Q: Solve the initial value problem y'=x^2-4x+3-6e^x, y(0)=8

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Q: Use the method of undetermined coefficients to solve the initial value problem x''+4x=3cos2t  ;…

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Q: Find the unique solution of the second-order initial value problem. y" + 8y = 0, y(0) = -1, y'(0) =…

A: Given differential equation is  y"+8y=0, y0=-1, y'0=2 Auxiliary equation is  m2+8=0⇒m=±22i So, the…

Q: Solve the initial-value problem xy′=y+x^2sinx,y(π/4)=0.

A: Simplify the given differential equation,

Q: Find the general solution of the DE y" + 4y + 4y = e²x

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Q: Solve the initial value problem xy‘ + 2y = 3x, y(2) = 3 for y = y(x).

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Q: (b) Solve the initial value problem z(0) - () |ã, #(0) =

A: firstly we find eigenvalues and then find corresponding eigen vectors and after that find general…

Q: Solve the given initial-value problem. y" + 4y' + 5y = 35e-4x, y(0) = -3, y'(0) = 1 y(x) = ???

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Q: Solve the initial value problem (x+ 2) y' = xy + 2y – 3x – 6 when x = 0, y = 1.

A: (x+2)y' = xy + 2y - 3x - 6  So, (x+2)y' = (x+2)y - 3(x+2)  So, (x+2)y' = (x+2)(y-3)

Q: 3) Find the solution of initial value problem -2x2 e 2yy' + 4.xy? y(0) = 1. 1+ x'

A: