3. Given the initial-value problem 2 = -y +a?e", +x²e*, 1< x < 2, y(1) = 0 with exact solution y(x) = x2(e* – e) - (a) Use Euler's method with h = 0.1 to approximate the solution and compare it with the actual values of y. (b) Use the answers generated in part (a) and linear interpolation to approximate the following values of y and compare them to the actual values. i. y(1.04) ii. y(1.55) iii. y(1.97)

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: Solve: x'y" - 7xy' + 41y =0

A:

Q: a)Solve the ecuation y''+3y'=12x-5 symbolic b)Solve the initial value problem y''+3y'=12x-5 where…

A: The given function differential equation is  y" +3y' =12x - 5 y(0) = 1,     y'(0) = 0

Q: a) 2xy dx+(1+x²)dy=0 b) y'+(4/x)y=x* ------by exact method ---by linear method

A:

Q: Find the general solution of the given equation y" + y = 0

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Q: Q1) Solve the following differential equations: 3. (x- 1)+ 2(x- 1)-4(x-1) + 4y = (1-x)?

A:

Q: the sho wh Solve innitial valve problem below: g/1-16y=e4x² g (0) = 10₂y '(a) = 7

A: The given equation is; y''-16y=e4x, y(0)=10, y'(0)=7

Q: (a) Given Bernoulli equation xy' + 3y = 6x³, solve for appropriate solution.

A: For the differential equation of the form, dydx+P(x)y=Q(x) , the integrating factor, μ(x) is…

Q: ) Verify that y=e-2x is a solution of equation x(y")3+ (y')4 – y = 0

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Q: Find the values of "r" for which y(x) = e* solves the equation y" +3y'-4y= 0

A: We have to find the value of r .

Q: 2. Compute the true solution to the problem Y'(t) = -e-tY(t), Y(0) = 1. %3D Using Euler's method,…

A: Given that, y't=-e-t yt, y0=1. Step sizes, h=0.2, 0.1, 0.05.

Q: 1) Find the general solution of the equation x³y"" - 2x2y" - 4xy' + 8y = x² + lnx.

A: In this question we will find the general solution of the differential equations.

Q: Q4. (a) Show that the substitution r= e' reduces the equation ar'y" + bry' + cy = g(x) to an…

A:

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. Compute the true solution to the problem Y' (t) = -e-Y(t), Y(0) = 1. Using Euler's method, solve…

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

A:

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: y" + 7y' + 10y = -1lte".

A:

Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

A:

Q: An Euler-Cauchy equation is given as x*y" +1.5xy – 0.5y=0, x(1)=5, 19 (9). 3 Solve the equation by…

A: Here, we have given that the Euler-Cauchy equation x2y''+1.5xy'-0.5y=0 and the initial conditions…

Q: M 3. Solve by using undetermined method Coefficients y" - Sy' + by = xe X of

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Q: Solve the give differnetial equation by undetermined coefficients y''' - y'' -16y' + 16y = 5 - ex +…

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Q: Q2 (a) Determine the solution of y" – y = e2x – x + sin x using method of undetermined coefficient.…

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Q: Find General Solution of y" + y" = 0.

A: Given the differential equation is y"' + y" = 0. Here the auxiliary equation is m3 + m2  = 0