а) x(0)--1,х' (0)-8 b) × () = },x (?) = o

Q: show that function  y1=x-1 is a special solution of the differential equation y'=1 - ( y-x+1)2 and…

A: Given the differential equation y’ = 1 – ( y – x + 1)2 and we have to show that y  = x -1 is a…

Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

A: The brine is entering more and going out less at rate (3 gal/min -2 gal/min = 1 gal/min), so…

Q: The general solution to a differential equation is given by y = c1e^(3x) + c2x. Suppose we then…

A: Solution:

Q: Find the particular solution that satisfies the initial condition: Differential equation: 2xy' - ln…

A:

Q: 20. x" +4x = 3e2"

A: We have to solve the differential equation using the method of undeterminedcoefficients and no…

Q: $2. x" – 4x' +3x =te".

A: Given that x''-4x'+3x=tet To find the general solution :

Q: Heat transfer from a body to its surroundings by radiation, based or he Stefan-Boltzmann law, is…

A:

Q: Create a third order, non-linear Ordinary Differential Equation with enough initial values to be…

A:

Q: Form the differential equation by eliminating A and B from Ax² +By² = 1.

A:

Q: Find the value of the arbitrary constant of the particular solution of the differential equation…

A:

Q: The differential equation formed by eliminating arbitrary constants a and 6: y = ax + bx+9 is

A: Given that

Q: Solve the differential equation x y' = In x-3xy with initial-value y(1) =2.

A:

Q: 5. By using separable differential equation, solve the initial-value problem 2x(y + 1)dx -y dy= 0,…

A:

Q: Find a first order differential equation for which y2 sin(xy) + (2xe)cos(x)) = 3 is an implicit…

A:

Q: Find the value of the arbitrary constant of the particular solution of the differential equation…

A:

Q: Show that the function  y1=x-1 is a special solution of the differential equation y'=1-(y-x+1)2 and…

A:

Q: Find the ordinary differential equation from the general solution: y = Ae-* + Be-*

A: Since you have posted multiple questions and we can answer one question. So, answered first…

Q: 1 Verify if y = -+; xy + y = x² is a solution of a differential equation.

A: We have to verify the solution

Q: Consider the initial-value problem (x² − 1)y"+y' + y = ex y(1) = 1 y' (1) = -1 Does the Existence…

A:

Q: Using the method of undetermined coefficients, a particular solution of the differential equation y"…

A: Given differential equation is y''-y'-2y=2 e-x   Let the particular solution of this differential…

Q: Show that the differential equation UTM dy -2 - ye rey - 2y dr is exact and find its solution.

A: Use the concept of exact differential equations.

Q: By using suitable method, form an ordinary differential equation by eliminating constant A from the…

A:

Q: What is the particular solution to the differential equation +1+y = 2e- with y = 1, 2=-1 when x = 0?…

A:

Q: Find a particular solution that satisfies the right-hand side of the above equation using the method…

A:

Q: 2. Test the exactness and obtain the general solution of the differential equation: 2+yexy y' =…

A:

Q: 2. What can you say about a solution of the equation y' = -25y2 just by looking at the differential…

A: Firstly we integrates, then solve it.

Q: у" - у' - бу %3D 0

A:

Q: Find two solutions in power series form of the given differential equation around the ordinary point…

A:

Q: From the differential equation by eliminationg the arbitary constant A,B from y=Ae/x+Be¬-7x +Be-7x

A: To form the differential equation by eliminating the arbitrary constant

Q: If the differential equation is = ye", where x = 0, y = e. Determine the value of y when x = 1.…

A:

Q: 4 By using separable variable method, find the general solution of the differential equation dy _y…

A:

Q: Find the differential equation by eliminating the arbitrary constant  x2-y2= 0

A: To find the differential equation x²-y²=0

Q: Suppose dr - =4sin(2x) and y= -2 when *=. what is the particular solution to the given differential…

A: In this question, we need to find the particular solution to the given differential equation.

Q: Use the method of Undetermined Coefficients to find a PARTICULAR SOLUTION to the differential…

A:

Q: Solve the differential equation with initial conditions y" - 3y 10y = 4e5t y(0) = 0, y' (0) = 1…

A:

Q: 3. Form a differential equation by eliminating the constants a and b: y = ax² + bx

A:

Q: Show that the differential equation dy -2 - yezy dr rezy – 2y is exact and find its solution. 3.

A:

Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

A: To Determine -

Q: The particular solution of the differential equation: et y" – 2y' + y =

A: Please see the explanation below

Q: What form of the particular solution is appropriate for the differential equationy'' - y'=4+4e*.

A:

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y ae" + be-ª.

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Find particular solution of the differential equation dydx-2x+13=4x+1y , given x=0, when y=0

A: I have solved using integrating factor

Q: Form a differential equation by eliminating the arbitrary constants A and B from the equation y =…

A: to find differential  equation we first form two Equation by differentiating y two times using…

Q: The number of arbitrary constants in the particular solution of a differential equation of third…

A:

Q: 26. x" +9x =5 cos , x(0) =0, x'(0) =0.

A:

Q: y' = ycotx + y²cscx

A:

Q: 3) Find the solution of the differential equation y = -ry + (/')².

A: The given differential equation is. y=-xy'+y'2                                .........1 This can be…

Q: Find the particular solution to the differential equation: dy/dx=3x^2cos^2y. Solution passes…

A: The given differential equation is in variable separable form. We solve the differential equation by…

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.