1. Compute the solution to the following initial value problem y' + y = x, y(0) = 1 Using Picard iterates with yo = 1. Compute the first 3 iterates y1, 92, 93-

Q: If y = u³ - 4 and u = 3x² + 10, find y' O 18x(3x² +10)² O 3x(6x² + 10)² O18(3x² +10)² 6x(3x² +10)² घ

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Q: 2) Use y = ax to solve 2'y" - xy' + (x+1)y=0.

A: The given differential equation is: 2x2y''-xy'+x+1y=0. We have to solve using y=∑n=0∞anxn+r.

Q: 2.. 16 0 -[]+[C] X 12 X'= e X = [X₁ ; X₂] Initial condition X₁(0)=1, X₂(0) = 1 find the solutions X…

A: What is Matrix Diagonalization: A square matrix can be decomposed into its diagonal form. The…

Q: Problem #1: Solve the following initial value problem. -2y₁ - y2 y/₂2 бу1 — 732 Y = = y₁(0) = 5,…

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Q: 4. Suppose the following functions are a general solution of: y(4) + a3y/" + azy" + a;y' + a0y = 0

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Q: .1) The general solution of the equation y" + y =-5e- , is: - y(x) = Ce-* + ez(Acosx + Bsinx) -e-* O…

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Q: Find the general solution of (1+ x²)y' + xy = x=1(1 +x²)-/½

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Q: Show by direct substitution that (-1)"+1 y = n-1 is a particular solution to (x + 1)y" +y' = 0

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Q: y'3 – (4x – 1)yy' – 4xy²y' = 0 Solve the equation by factoring. |

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Q: Find the iterative scheme for the root of equation x' +3x-4 = 0 by iteration method near to 1.2. .a…

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Q: 9. Find the general solutions of X' = AX with A =

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Q: While calculating the approximate solutions of the equation x² – 2x – 3 = 0 using the initial value…

A: In the iteration method is used to estimate the roots of the function f(x) the first step is to…

Q: Let A 22 - (²²) 11 Find the solution of the problem: x), Y(0) = = - (8) -X Y' = AY +

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Q: 3 6. Let A = -4 Find the general solution of x' Ах.

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Q: Solve the following initial value problem -7 4 | y' = У, у (0) - -6 7

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Q: Solve the following Higher Order Non-homogenous DE using Methods of undetermined coefficients…

A: Given,y'' -2y' +y=3x+2A second order linear, non-homogeneous ODE has the form of   ay''+by'+cy=gxThe…

Q: 1. Describe and solve each first-order equation. 2 2 (a) x²y'=xy²+3y² (b) y'+3y=3t²e-30

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Q: 8. In a permanent disability model, we have = 0.2, t = 0.1, pt = ,01 ,02 12 0.25 healthy (0)…

A: Given  μx+t01=0.2,  μx+t02=0.1,  μx+t12=0.25

Q: 2.2. Solve the following initial value problems: a) t+2y=², y(2)=1.

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Q: 7. Verify that y = x2 - 1 is a solution of (y')* + y? = -1.

A: Given- y=x2-1 To verify- That the above function is the solution of y'4+y2=-1.

Q: This is the fourth part of a four-part problem. If the given solutions 7₁ (t) = - [²2²], 1₂(t) -…

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Q: 5. Find the critical numbers. y= x5/3 – 3x2/3

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Q: y' 3x² + 4x - 4 2y-4 y (1) = 3

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Q: 3. Suppose = f(). (a) Given y(xo)= Yo, when does this equation have a unique solution? (b) Make a…

A: suppose dydx=fymx (a) given yx0=y0, when does this equation have a unique solution? we have  y'=fymx…

Q: 3. Find the general solution of the following DE. y' = 3 (y + 1) O y = ce³x - 1 3y = ce³x - 1 Oy =…

A: Use variable separable to Solve this problem.

Q: Find xp(t) only for the following, check for any duplication. x'= 5x-6y+8 y'=x-2y-4e¹

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Q: 24. 2x²y" + 3xy' + (2x – 1)y = 0

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Q: 4. Find the solution of the IVP y" – 4y' — 12y = 3e5x, y(0) = 18 7' y' (0) = -1/₁

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Q: A1.1 1. y= Ae²x + Be-x

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