FIND solution of the following initial value problems: ור5ס a) y' + 2xy = f(x), y(0) = Your Registration f (x) = {x, 0 Sx<1 lo, x > 1'

Q: Find the particular solution for initial value problem.

A: x2dydx-yx=0⇒x2dydx=yx⇒dyy=xx2 dx⇒dyy=x12·x-2 dx⇒dyy=x-32 dx Now integrating on both sides, we get…

Q: 12. Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the…

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Q: 3) Find the solution of Initial Value Problem dy 2x-sin y dx 2x cos y ; y(4)=0

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Q: 4. (a) Show that the solution of the initial value problem y = 1+y. y(0) = 0 is y(r) = tan z.

A: y'=1+y2 Given to show that this initial value problem on solving gives y=tanx

Q: Solve the initial-value problem (2y sin x cos x + y sin x)dx + (sin'x-2y cos x)dy 0 by using…

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Q: Problem 2.3 i. and 2.3 ii

A: Given initial problems are

Q: Find an explicit solution of the given initial-value problem. (1 + 1*) dx +t (1 + 4x²) dt = 0, x (1)…

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Q: Use Euler's method with step size 0.3 to estimate y(1.5), where y(x) is the solution of the…

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Q: Find explicit particular solutions of the initial value problems in Problem dy х. dx - - y = 2x²y,…

A: Given differential equation can be written as

Q: What integral equation is equivalent to the initial value problem y′ = ƒ(x), y(x0) = y0?

A: Write y'= dy/dxThen separate the variables.

Q: Use Euler's method with step size 0.4 to estimate y(0.8), where y(x) is the solution of the…

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Q: 3. Consider the Initial value problem ry' = y + r ln(r); y(1) = 2 (a) Estimate y(1.5) using Euler's…

A: We have y'=yx+ln(x), y(1)=2, h=0.25, y(1.5)=? f(x, y)=yx+ln(x),   x0=1, y0=2

Q: Example 35. Using th d²y satisfying the differential equation v(1) = 2. + y = x, subject to the…

A: Here we need to use finite difference mthod.

Q: Consider the initial value problem y'(t) = t² - 3y, y(3) = 1. What is the approximation to y(3.1)…

A: Here we have to use the Euler's method.

Q: Find the particular solution of the differential equation dr/ds = er−2s that satisfies the initial…

A: Given: drds=er-2s,  r0=0

Q: Use variation of parameters to solve the given initial-value problem. x'=(³₁3¹)x+ (4²).X (0) = (¹)…

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Q: Solve the initial value problem y" – y = 2 – t² with initial conditions y(0) = 1, y'(0) = 0. %3D

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Q: 2. Solve the initial value-problem: . dY dt Y with Y(0) = (1,0). - 4

A: The solution is given as

Q: Consider the initial value problem y" + y = fk (t), y(0) = 0, y'(0) = 0,

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Q: 5) For the initial value problem y'(t) = y + ty, y(0) = 1, use Euler's method with time step At =…

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Q: 3. Consider the initial value problem (IVP): ty' — y = t²e-t, y(1) = −1. (a) Use integrating factor…

A: We will use integrating factor method to solve this.

Q: Solve the separable initial value problem. 1. y' = In(x)(1+y²), y(1) = 1 → y= 2. y =…

A: Use the following formulas 1.∫xndx=xn+1n+1+c2.∫11+x2dx=tan-1x+c3,∫ln x dx=xln x-x+c

Q: 9. Find the particular solution for each initial value problem. a) (2x + 3)y = where y(0) = 1 dx b)…

A: Particular solution:         The solution obtained by giving particular values to independent…

Q: Use Euler's method with step size 0.2 to estimate y(0.4), where y(x) is the solution of the…

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Q: Consider the Initial Value Problem: y = y + 3x – 5, y(1) = -2. An approximation of y(1.2) with step…

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Q: Denote the Euler-method solution of the initial- value problem dx dt x(1) = 1.2 In x using step size…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: Find an explicit solution of the given initial-value problem. () - 1 dx 3(x2 + 1), dt X =

A: Given query is to find the solution of the differential equation.

Q: 3. Find an explicit solution of the given initial-value problem. dx 4(x + 1), x(7/4) = 1 dt 2 dy y…

A: By bartleby policy first question onpy unless asked otherwise.

Q: 5. Given the initial value problem dy dt t(y + 1), y(0) = 2 use Euler's method with at least four…

A: Euler's Method is used

Q: 1. Solve the initial value problem, (1/x +2y²x) dx + (2yx² – cos y) dy = 0, with y(1) = x.

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy + 2xy = f(x),…

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Q: Solve the initial value problem 2 4 6 0 2 1 0 0 4 1 dX Х, X(0) - 1 dt 1

A: On comparing with  dXdt=AXA=246021004

Q: Solve the initial value problem. nt 7y – 2y = e-, y(0) = Let a, be the value of a for which the…

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Q: 1. Solve the initial value problem = yr - 1.1y over the interval from t= 0 to 2 where y(0) = 1 using…

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Q: Solve the initinal - value problem dy dx » y(6)=0 COsx - Sinz +y 0Lx s0.5 Using (a) Com pute the…

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Q: Find an explicit solution of the given initial-value problem. 1 √1-y² dx √1-x² dy = 0, y(0) = = y =

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Q: 1. Find the value of x(0.5) for the initial value problem ,x(0) = 1 using Euler's method dt with…

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Q: 2.3.4 Find the value of X(1.1) for the initial-value problem dx dt =-xt, x(1) = 0.1 using Euler's…

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Q: Find the serial solution of y''+xy'+y=0 ; y(0)=0, y'(0)=0 initial value problem adjacent to the…

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Q: Consider the initial value problem: y-y+8, 0sts 1, y(0)-1 The approximation of y(1) by using…

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Q: Use Euler's method with step size 0.1 to estimate y(0.5), where y(x) is the solution of the…

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Q: Use the method of integrating factors to solve the given initial value problem.…

A: The given equation is

Q: 4. Test the existence and uniqueness of solutions of the initial value problem: dy 2xy y(-1) = 1 dx…

A: The given differential equation is dydx=2xy4+x2+y2.      y(-1)=1. To Check: Existence and uniqueness…

Q: What is the particular solution to the dy dx a°+3 with the 3y differential equation initial…

A: The differential equation dydx=x2+33y is separable because it's the form of dydx=f(x)g(y) where…

Q: Solve the separable equation y = 2/y In x, y(e)=1. (initial value problem)

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Q: 4. (a) Solve the initial value problems, dy = sin t + 1; yE)=; dt (b) Evaluate V1 – x² dx. |

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Q: Find the solution to the initial value problem ry' = y + In(x), y(1) = 0.

A: The objective is to find the solution to the initial value problem.