The solution to this IVP: y'' + 8y' + 16y = 0 with these initial conditions: is: y(0) = 4_and_y'(0) = − 21

Q: 8. y" – y = 5sin²(x); when y(0) = 2, y'(0) = -4 %D

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Q: 15. Let 2 √x 4 3/2 y' = 2y + 2xy' 13/2 Solve for y' when x = 1 and y = 4

A: NOTE: Refresh your page if you can't see any equations. . here we have x=1 and y=4

Q: A -3 0 1 -3

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Q: valuate the following: a. L {e3t + cos6t - e3t cos6t} b. L-1 {6s/(s2 + 25) + 3/(s2 + 25)} c. L-1…

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Q: Suppose that Yı x5 is a solution to x²y" – 10xy' + 30y 0. Use reduction of order to find another…

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Q: As the number of hours since you ate protein increases from 2 to 2.75 hours what is the average rate…

A: Given: At 2 hours B1=1100 mg/L At 2.75 hours B2=1025 mg/L

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: Q1. Find the general solution for the non-homogen 1st OLDE using undetermined coefficient method.…

A: Given Y'=-3-456Y+5-6ex

Q: Obtain general solution. 1) y''-y=ex-4

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Q: 5. Solve, using the method of undetermined coefficients: y" + 2y' = 2x + 5 – e-2= %3D

A: First we shall get particular solution of y''+2y'=2x+5. Using method of undetermined coefficients y…

Q: y(4) - 4y" + 6y" - 4y+y=0; y(0) = 0, y'(0) = 1, y'(0) = 0, y" (0) = 1

A: The Laplace transform is used to find the solution of the linear ordinary differential equation with…

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

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Q: In(-/-) (vi) 2x In - x = 0

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Q: y = C¡e e-2= + Cze³* + C2e%

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Q: Find the general solution of x2y" - (2a-1)xy' + a²y = xa+1 where a is a constant.

A: Given  x2y'' - 2a - 1xy + a2y = xa+1  ----------(1)           This is Cauchy's homogeneous…

Q: 6. Solve the IVP with y(1) = 2 and ty' = 4t² - 2y.

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Q: 3 ť'y" +7t y' +1o yoo

A: A detailed solution is given below

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: For the difference equation given by y(k + 1) + y(k) = 3 (1/2)* with y(0) = 1 Find the expression of…

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Q: 2.ryy' = y? - 2x. Find the solution that passes through the point (1,2).

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Q: (1) y "'+ y "– 2y = 3+2cosx

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Q: Q4- Solve y"- 4y' + 13y 3x.e*

A: Topic:- differential equations

Q: Find the general solution to

A: Given:              y'+yx=1x4y34 To find: The general solution of the given differential equation.

Q: - Sapotri to solve 2x?y" – my + (x + 1)y = 0. n=0 12) Use y =

A: Given: 2x2y''-xy'+x+1y=0. To Do: Solve the given differential equation using y=∑n=0∞anxn+r.

Q: j'+7y'+12y=2le", y(0); (0)=,"'(0)= -10. 10)=-10 .

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Q: Use undetermined coefficients to find the particular solution to y''−9y'+20y=−1768sin(t)

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Q: 1. Verify x₁ = t²x² = (' -3t 5 3t+²) and x2 = 5t 3t² -2t X. t -t-> - are solutions to

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Q: The general solution to the ODE x²y" + 2xy' - 2y = 0 is y = C1x + C2x-2. Use variation of parameters…

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