y(t): Solve the initial value problem a = 49y" +84y +36y= 0, y(0)= a>0, y'(0) = -1. Find the critical value of a that separates solutions that become negative from those that are always positive.

Q: Solve: y''+ 6y' +5y = 20t + 39 y(0) = - 4, y'(0) = 19 | y(t) =

A: The solution is given as

Q: 4x y" - 5y + 4y = ¹, y(0) = 0, y'(0) = 10/3 e

A: Please find attachment

Q: Solve 4y'' + y' – 3y = 0, y(0) = - 4, - 4, y'(0) = 0.5 y(t) =

A: The given differential equation is second order linear homogeneous differential equatio. So firstly…

Q: solve using method of undetermined coefficients 2y'+4y=3cos(2t), y(0)=0

A:

Q: Determine by substitution if y(x) =xe* is a solution of y"- 2y' +y = 0 %3D

A: Given  The differential equation is y''-2y'+y=0

Q: Solve 2y'" + 9y' + 4y = 0, y(0) = 8, y'(0) = 14.5 %3D y(t) =

A: Given 2y"+9y'+4y=0 ; y(0)=8 ; y'(0)=-14.5 We need to solve the given differential equation.

Q: (B) Find the general solution of x²y" - (2a-1)xy' + a²y = x²+¹ where a is a constant. Good Luck

A: This question is about ordinary differential equation.

Q: Solve y + y = 2y = 0, where y (0) - = 3 and y (0 y(t) =

A: y''+y'-2y=0 Auxiliary eqaution m2+m-2=0

Q: Solve 2y"+7y'+6y= 0, y(0) = 7, y'(0) = −13 y(t) =

A:

Q: (c) xy' + 4y = 3x², y(2) = 4

A:

Q: Find the general and particular solution of the y"=3e³x if f(2)= k and f'(2)=k²

A: y"=3e³x if f(2)= k and f'(2)=k²

Q: Solve y" + y = 8(t – 7) – 8(t – 27), y(0) = 0, y' (0) = 1.

A:

Q: Determine the solution of y' = - given y (0) = 17 ху

A:

Q: Find the solution: y" + 3y' + 2y = 12x2; y(0) = a, y'(0) = b

A: We have to find the solution to the given equation.

Q: Solve (c) y" + 4y = 0, (d) (1+y/2)3 = (y')².

A: Solution is given below:

Q: y = xy' – y* + 1 find general solution and particular solution.

A: Given, We have to find general and particular solution for it. Working:

Q: Solve: y'"' + 4y'' + 5y' + 2y = 0 y(0) = 4, y'(0) y(t) = = 4, y''(0) = 5

A:

Q: 2. Use separation of variables to solve (a) y' = -2y, y(0) = 1 (b) 4y' = y², y(0) = 4 %3D (c) y' + y…

A: Note:  "As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: Solve for the general solution: y" + 3y = x + 1. Oy(x) = C₁ + c₂e-3x + 2x/9 + x^2/6 y(x) = C₁ +…

A:

Q: Use undetermined coefficients to find the particular solution to y''+ 7y' + 10y = 3e Y(t) =

A:

Q: Find the general solution to  y''+ y' = 1 + 2sin(2t)

A:

Q: The general solution to: y'' – y' + 4y = 0 %3D is: y(x) = %3D Typle c_1 and c_2 to get c1 and c2 and…

A: We have to find the solution

Q: xy' + 2y = 3x, y(1) = 5 %3D

A:

Q: wherey = x + C is a solution to this DE. What is the particular solution?

A: Let's find.

Q: mit equatio x²y' + 2xy + O with respect to x and solve for y'. Skip (you cannot come back) x²y + xy²…

A: Given query is to find the derivative.

Q: (B) Find the general solution of x'y" + xy' -y=x²+1 given that y, = x is a solution of the…

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Q: 2) Find the general solution to 2y" - y' - 6y = 0. Find the particular solution that satisfies y(0)…

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Q: If y = f(x) is the solution of y" – 9y" +26y' – 24y = 0, f(0) = 4, f'(0) = 15, f" (0) = 44, then

A:

Q: Find the solution of y" - y" + y' — y = 0, ƒ(0) = 1, ƒ'(0) = 3, ƒ"(0) = 1.

A:

Q: Solve y’’ – 4y' + 85y = 0, y(0) = 2, y'(0) = y(t) = - 41

A: