Solve the initial value problem : 2ry = x² + 2y² with y(1) = 3

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

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Q: Solve the initial value problem; る+y ク(o)= 4 ニ6

A: The given differential equation is  y' + y = 0 y(0) = 4

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

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Q: Solve the initial value problem given by y" – 4y' + 13y = xe", y(0) = y'(0) = 0 -

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Q: solve the given initial-value problem: y′′ − y = 9xe2x , y(0) = 0, y′(0) = 7.

A: Consider the given differential equation: Here the objective is to find the solution of a given…

Q: Solve the initial value problem dy_ ry+ y² dr y(1) = 2.

A: Given equation dydx=xy + y2x2 .........(1) is a homogeneous differential equation .  Since if we…

Q: solve the problem with given initial value, y''-6y'+9y=0, y(0)=0, y'(0)=-2

A: Given y''-6y'+9y=0, y(0)=0, y'(0)=-2

Q: Solve the initial value problem y' – 2.ry = 2xe V, y (0) = 1 and verify that the solution is true.

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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 y′=2y2+xy2,y(0)=1

A: Given an initial value problem,y′ = 2y2+xy2, y(0) = 1

Q: Solve the Initial value problem x' -x=8(t-2),x(0) =x' (0) =0

A: We use the Laplace transform to solve the given initial value problem.

Q: Solve the initial value problem y"+ 4y = 2x; y(0) =1,y'(0)=2

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

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Q: 4xyy’ = y^2+x^2 y(1)=1  find the specific solution of the initial value problem

A: We will solve the problem.

Q: =) Solve the Initial value problem: + 3y² /x² + 1 = 0, y(0) = 1

A: Use separable variable method

Q: Solve the initial value problem. 1. y'=4xe2x²cosx - ytan x, where y(0)=1

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Q: Use the method of undetermined coefficients to solve the initial value problem. y" + 4y = 1² + 4e¹',…

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Q: Solve the initial value problem, y" + 6y' + 25y = 0 where y(0) = 1 and y' (0) = 5.

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Q: dy Solve the initial value problem: + 2y = 6e¬x; y(0) = 8

A: Since the given differential equation is first order linear differential equation so we first find…

Q: Solve the initial value problem 2x(y+1)dx - ydy = 0, where x = 0 and y = -2

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Q: Solve the initial value problem below. x²y'' – 6xy' + 12y = 0, y(1) = - 4, y'(1) = - 17

A: We have to solve the given initial value problem.

Q: dy 4. Solve the initial value problem x + y = 3x2, y(1) = 3.

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Q: Solve the initial value problem  y′=8cos(8x)3+2y, y(0)=−1 and determine where the solution attains…

A: Given y'=8cos(8x)3+2y, y(0)=−1

Q: Find the solution of the initial-value problem dy +3z*y = r², y(0) = 2. dr

A: We have to solve given problem:

Q: Determine if y=e−x+8x−9 is a solution to the initial value problem given by y′+1=8x−y and y(0)=−8.

A: The given differential equation is y′+1=8x−y.The solution of the deferential equation is given as,…

Q: Solve the initial-value problem. y′ + 2y = 1, y(0) = 1

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Q: Is y=e3x−2x−3 a solution to the initial value problem shown below? y′−3y=6x+7 y(0)=−2   Yes or no?

A: Yes

Q: solve the Initial Value Problem. y' + 3y = e2x , y(0) = −1

A: We first find the integrating factor  Then we multiply both sides by the integrating factor (I.F.)…

Q: Find the solution of the initial value problem y′+3y/t=t2,y′+3y/t=t2, y(1)=1/2

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Q: = 3e*, y = 6, when x =

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Q: solve using the Initial Value Problem.  xy' + y = ex ,       y(1) = 3

A: Given,

Q: Solve the initial value problem y' = xe ; y(-1) = 3

A: We can solve the initial value problem as below.

Q: Use the method of undetermined coefficients to solve the initial value problem. y" + 4y = ² + 4e¹,…

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Q: Solve the initial value problem  y′=y2,y(0)=1,y′=y2,y0=1, and determine the interval in which the…

A: Solve the initial value problem y'=y2, y0=1 & determine the interval in which solution exists.

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 initial value problem y' = (x + y – 1)² with y(0) = 0. %3D

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Q: Find the real-valued solution to the initial value problem -3 x'(t) = x(0)

A: Given: X't=-32-1-1x and initial value is X0=1-2

Q: Solve the initial-value problem: y′′−y′−2y =15e2x, , y(0)=0, y′(0)=8.

A: Given a differential equation, y′′−y′−2y =15e2x,                    .....(1) It can be written as…

Q: Solve the initial value problem using y"+3y'+ 2y = 2u(t-2).y(0) = 0, y (0) = 0

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Q: y' = 3y2 y(2) = 0

A: For first order differential equation of variables x and y, if it is possible to arrange all the x…

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

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Q: solve the problem with given initial value, 9y''-12y'+4y=0,  y(0)=2,  y'(0)= 1

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

A: Simplify the given differential equation,

Q: ) Solve the initial value problem y'- 2ry = 2xe Vy, y (0) =1 and verify that the solution is true.

A: We need to solve the given initial value problem. The solution is given below.

Q: Solve the initial value problem yy' + x = y(1) = √15. + y² with

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Q: 3. Solve the initial value problem V1- y² | y(e") %3D || 2

A: We can use the application of integral in order to solve the given problem.

Q: Solve the initial value problem y = 8x*e=2w, y(1) = 0..

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Q: Solve the Initial Value Problem. y = 9x (y +9), y(0) = 0 %3D

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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)

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.