The solution of the differential equation given by x¨ − x = sinht, with x (0) = 0 and x˙ (0) = 0, it is given by Select one:

Q: Find the value of b for which the differential equation 5xy (yešey + x) dx + (bæe*v) dy = 0 is…

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Q: Find the general solution of the differential equation. Use a graphing utility to graph three…

A: Given ODE

Q: a) Solve differential equation dx (y² – 4)(x – 1) = (x + 1): dy

A: Solution of the problem is given in the next step.

Q: The solution of the differential equation given by ë + i = et, with ¤(0) = 0 y ¿(0) = 0, it is given…

A: to find the solution to the differential equation we use the formula y=CF+PI  Where CF is the…

Q: 3xy dy (In y)8 da

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Q: Determine whether given differential equation is exact. If it is, find the solution. (5x + 4y) dx +…

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Q: a) (2 - 1)y = y² – 1, yı (2) = 1

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Q: Find the general solution of the differential equation: y' - 5y = et Use lower case c for the…

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Q: determine the value of k that will make the equation exact and solve the resulting differential…

A: we are asked to find the  value of k

Q: Solve the differential equation with the appropriate method. Finalize answer free of fractions,…

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Q: The indicated function y1(x) is a solution of the given differential equation. Use reduction of…

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Q: Find the general solution of the differential equation: y'-5y = et Use lower case c for the constant…

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Q: When a differential equation is said to be exact? Solve the differential equation (2x cos y + 3xy)dx…

A: Let us consider the differential equation of the form Mdx+Ndy=0 To solve the differential equation…

Q: Solve the Differential Equation subject to Þ(0) = 0. Write final answer in explicit form.

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Q: Given the differential equation -(승) (중), y" Find two values of r such that y = x' is a solution of…

A: The given differential equation is y''-6xy'-8x2y=0. Let y=xr. This gives  y'=rxr-1     and…

Q: dy - y = xy2 dx

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Q: Given the DE as 2xy² + 4 = 2(3 − x²y)y'.

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Q: Show that the differential equation below is an exact differential equation, and solve the general…

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Q: Find the general solution to the differential equation using the method of Undetermined…

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Q: 1. 7ху' — 2у + (E) - = 0

A: Given differential equation  7xy'-2y+xy6=0

Q: .2e*cotydx + (1 + e*)csc²ydy =

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Q: Solve the differential equation for y if (1+9x²) dx %3D

A: Here we have to solve the differential equations,  1+9x2dydx=1.................................(1)

Q: 1. The linear differential equation dx has the integrating factor equal to (Note: Simplify or solve…

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Q: 16. х" — 7x'— 51 — 3.

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Q: The Differential Equation y'+y=e* has a solution y=(x+C)ex C is an arbitrary constant. IF TRUE, show…

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Q: Solve the given differential equation. All solutions should be found. 2xy + y² + 8 x² + 2xy dy dx…

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Q: When solving the following differential equation with the initial condition by the separable…

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Q: Solve the differential equation with appropriate method. Express final answer equated to y^n. (e.g.…

A: Given, The differential equation dydx-y=xy2 We have to solve the differential equation.

Q: a) Solve differential equation dx + 2 dy x³ cos y %| - y

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Q: Using separation of variables, solve the differential equation, dy -cos² (x) = 0. dx sin(x) – Use C…

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Q: Yp = -1 / 5ex - 1/2 (cos 2x) ((ln (sec2x + tan2x)) is the particular solution of the differential…

A: A solution yp(x) of a differential equation that contains no arbitrary constants is called a…

Q: Using the method of undetermined coefficients, find the general solution to the differential…

A: The given differential equation is y′″ - 3y″ - y = 4et                                    ...... (1)

Q: Solve the differential equation dy = a da; if the curve passes through (1, 0)? General Solution…

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Q: Solve the differential equation xy' - 3y = 2x° In x. The solution is y = (Type an expression.)

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Q: (y')³.x – (y')².y – 1 = 0

A: Assume y'=p, write the given equation in terms of y then differentiate the equation with respect to…

Q: Use substitution to find a general solution of the differential equation  a)  x^3*y'+x^2*y=y^2…

A: We need to convert Bernoulli equation into linear differential equation form by using substitution

Q: 6. If y = x (In x), find d²y / dx².

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Q: Solve the Differential equation

A: To find the solution of the differential equation given

Q: Solve the differential equation with appropriate method. Simplify final answer the simplest…

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Q: 4. When solving an auxiliary equation of a certain differential equation the roots m = 1 ± 2j are…

A: I am attaching image so that you understand each and every step.

Q: 2) x- 1= -0y

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Q: Solve the differential equation using the Method of Undetermined Coefficient. Show your solution.…

A: Differential equations

Q: y'-5y= x'e* – xe* ito

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Q: One solution of the given differential equation is given. Use the reduction of order formula to find…

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Q: By solving the differential equation: 33 y = (x – 8)y' + (y')* It is obtained, as part of its…

A: We are given the following differential equation.           y=x-8y'+y'33 We further have that…

Q: Find general solutions of the differential equation. If an initial condition is given, find the…

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Q: xy (prime) – 2y = 8x² ln x

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.