(a) By inspection, find a particular solution of y" + 2y = 14. Yp(x) 11

Q: Find y" for y = 4+ X y" =D

A: Taking first derivative,

Q: Verify whether y(x) = 2e-*+xe-* is a solution of y" + 2y + y = 0.

A: Topic = Differential equation

Q: What are the solutions of the equation 2sin(4x)=1 on the interval [0,n)?

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Q: 5. [10 points] Find the general solution y"-6y' +9y = x*e*

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Q: Solve the following linear differential equation system, i.e., find y₂(t). dyn (1) dt dyż (t) dt =…

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Q: Find the general solution to y'" + y = 0 Show the solution.

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Q: 2. Find all solutions to the equation y" +y – 10y = 0. Hint: p(A) = X3 + A – 10 = (X – 2)X² + 2A +…

A: The solution of homogenous linear differential equation of constant coefficient is find by…

Q: d. y= x² + y x + cos y

A:

Q: s of stick t

A: Given that it needs 5meters of stick to make a picture frame.

Q: 9. y" +9y = 0

A:

Q: Find a particular solution to y" + 5y + 4y = -10te". Yp =

A: Given the D.E. y''+5y'+4y = -10te3t We have to find particular solution yp of this equation.

Q: Find a particular solution to

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

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Q: 3. Show that y = 5x2 +2 is a solution to the DE ry' +y" = 2y.

A:

Q: y" – 2y' + y = -3 – x + x?.

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Q: DETERMINE SOLUTION OF 1 x dy dx + y = x² + x (2x+3y-13) dx + 3x - 2y) dy = 0 DE

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Q: Find the general solution to 3x y" + 9y= e³x + secx.

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Q: The function f(x) = |ax - b| + c|x| : x in (-∞, ol where Find the

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Q: ) Find the general solution: x" - 9x = 0

A: The given differential equation is       x'' - 9x =0      Then auxiliary equation is     D2 - 9=0…

Q: 1 Q6 Solve y" + 3y + 2y = 1² 1+e

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Q: Find the general solution for y"" + 2y" + 2y' = 0

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Q: Evaluate the general solution of y""=e4x + sinx

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Q: x2 (4) Calculate the result of the equation Having x= 0 , 1 , 2 /5+ x

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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: xy" + xy² + 4y = /Nx Find the solution y(x)

A: We will find the solution of the differential equations.

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

A:

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

A:

Q: What is the solution to y' +2 = xy3? * +c a. b. = -x +c c. xy? = - +c d. xy = -x² + c e. None of the…

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Q: Find the solution of y" – y – 6y = 48 et with y(0) = 7 and y' (0) = 3.

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Q: 3) y +2/u

A: Given: y+2y=x