Find the solution of the given initial value problem in explicit form. 1 y' = (1 - 11x)y², y(0) - - 9 y(x) =

Q: Find the general solution to y''-1=0

A: y''-1 =0y'' = 1y' = ∫1 dxy' = x + By =∫(x + B) dxy = x22 + Bx + A

Q: The unique solution to the initial value problem is y(t) = 2e-5t - 8t – 5. Determine the constant yo…

A:

Q: The unique solution to the initial value problem is y(t) = 9e−²t + 4t + 7. Determine the constant y…

A:

Q: The general solution of y' x2 can be written in the form

A:

Q: Find a particular solution to the given higher-order equation. y'"' - y'' - 22y' +40y = - 40t²…

A:

Q: How do I find the particular solution yp in the equation above?

A: For particular equation we will crate function for particular integral. Then we solve it by using…

Q: 3. Solve each equation. y(0) = 1, y' (0) = -1 (a) y" + 4y = 0, (b) y" + 5y = 0

A: We have to solve given problem:

Q: Find the general solution of y""- 5y"- 6y'=0

A: The given differential equation y'''-5y''-6y'=0

Q: Find the general solution y''-y'-2y=0

A: Given the differential equation y''-y'-2y=0. We need to find the general solution of the above…

Q: Solve y'' − 4y' + 4y = 3e2t

A: Solve y'' − 4y' + 4y = 3e2t

Q: 1. Solve the equation y2 + 6x = y(3y – 2x)y'

A:

Q: Solve by undetermined coefficients. y" – 3y' = 6e – 2e", y(0) = 0, y (0) = 0.

A:

Q: 1. Find a general solution of the first order equation: y'= 3x²y².

A: The given first order differential equation is solved by method of separation of variable.

Q: Solve (2x – 1)3y" + (2x – 1)y' - 2y = 8x? – 2x + 3 %3D |

A:

Q: [  y'''- y' = ex - 2x  ] Please find a particular solution yp for the above.

A: Particular Solution: Consider the equation Let be the differential operator Then equation (1) can…

Q: Find the general solution of the given equation y''  - 9y = 0

A: From the given data:

Q: Find the general solution for the problem in the form y=yc+yp y'' - 3y' - 4y = 2 + 6t + cost

A:

Q: Solve x'y-5xy+13y-0

A:

Q: Solve the IVP by substitution. (3x2 - 2y2)y' = 2xy;  y(0) = -1

A: Substitute  x = vy and than solve using method of separation of variables.

Q: ii) Solve (x D²– 3xD+4) y = x² given that y(1) =1 and %3D - y'(1)= 0.

A:

Q: 4. Solve (x-2)y" - (4x-7)y' + (4x-6)y= 0, if y₁ = e2x is one known solution? HO The Cystem 2e²t

A:

Q: What is the general solution to y''+y=0. Show the solution.

A:

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