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

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

A:

Q: x + 4y3) dy- ydx = 0

A: We have to find the solution of the given non exact differential equation.

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

A:

Q: Help

A: In such problems ie second order linear differential equations when we are given one solution,y1 we…

Q: (b) Form the differential equation by eliminating the arbitrary constants a,b from y = aez + be 8z

A: Differentiate twice with respect to x then we get the answer

Q: Find the particular solution to the differential equation. 4y2 dx = 3x2 dy    when x = 4, y = −1

A: The objective is to find the particular solution of the differential equation.

Q: Find general solutions of the differential equation    (x+y)/y'=x-y

A:

Q: By using substitution of x-e' and t = ln(x), find the general solution of the differential equation.

A:

Q: The universal solution of the differential equation below may be found by substituting y=zx. Hence…

A: Given that                       x2 dydx = y (x+y)   hence we have to find the solution of d.E

Q: Solve for the particular solution of the non-homogeneous differential equation. 1. y''=4

A: Solution :--

Q: Consider the differential equation: 1 y" – y = What is the general solution?

A: We have to find the general solution of the given problem.

Q: Eliminate the arbitrary constants: y= x+ Ce2x + C2e¬x 1.

A:

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

A:

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = a sin x…

A: Eliminating arbitrary constants a & b using derivatives.

Q: Find the differential equation by eliminating arbitrary constant  y=Ae-3x+Be2x

A:

Q: particular

A:

Q: Explain how to solve a separable differential equation of the form g(y) y'(t) = h(t).

A: A separable differential equation is one in which the terms of two variables in the term can be…

Q: Find the particular solution that satisfies the differential equation and the initial condition. x²…

A:

Q: Determine the solution to the differential equation given by: y''-2y'+y=sin x

A:

Q: solve the for the general solution of the differential equation( linear homologous equation): y''-…

A: answer  Y = 9x22+ 3x detailed solution is given below

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: Solve the differential equation by variation of parameters, subject to the initial conditions y(0) -…

A: The given differential equation is, y''+2y'-8y=5e-2x-e-x. Obtain the homogeneous solution.…

Q: Find the particular solution that satisfies the differential equation F'(X) = 10x − 12x3 with an…

A: Given the differential equation: F'x=10x-12x3 Initial condition: f3=2

Q: 2. Form the differential equation from the family of curves y² = Ax² – Bx² , where A and B are…

A:

Q: Find the differential equation of the family of cissoids: y^2 = x^3/ (a-x)

A: Perform the differentiation and eliminate the constant term in the differential equation to obtain…

Q: Determine the appropriate form for yp on the differential equation y" = 9x^2 + 2x - 1 %3D

A:

Q: Determine the value of C for the given first order differential equation when x-2 and y=1. e#+v/ =…

A:

Q: Form the differential equation by eliminating arbitrary constant  y=Ae-3x+Be2x

A:

Q: Solve the differential equation using only methods taught in class. y' + 3xe' = 0

A:

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

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

Q: Find the two power solutions of a given differential equation about the ordinary point x=0. 1.…

A:

Q: Determine if the function is a solution of the differential equation y''-y=0

A: y''-y=0 y'' represents the second derivative  we find the roots , by writing the given equation in…

Q: Determine the particular solution that satisfies the differential equation and initial condition…

A: General solution of the differential equation

Q: 2) (x²y³ + y)dx + (x³y² – x)dy = o

A: (x2y3+y)dx+(x3y2-x)dy=0 this is an exact equation  M(x, y)= x2y3+y N(x, y) = x3y2-x We will evaluate…

Q: Find the particular solution that satisfies the differential equation and initial condition. x2…

A:

Q: use the method of variation of parameters to find a particular solution of the given differential…

A: solution:-  The given differential equation is  y''+4y=cos3x The auxiliary equation of above…

Q: Find the particular solution that satisfies the differential equation and the initial condition.…

A: To find The particular solution that satisfies the differential equation and the initial condition.

Q: Solve for the particular solution of the non-homogeneous differential equation. 1. y''-2y'=ex

A: Solve for the particular solution of the non-homogeneous differential equation. 1. y''-2y'=ex

Q: Use the initial condition to find the particular solution of the differential equation. differential…

A:

Q: Find the particular solution of the differential equation satisfying the initial condition…

A:

Q: The differential equation: y²x + y² = x²yy' is solved by

A:

Q: y' = ycotx + y²cscx

A:

Q: Find the particular solution to the differential equation y′ = 4x + 3 passing through the point…

A: To find: y'=4x+3dydx-4x=3       dydx+Py=Qwhere P and Q are variables of x onlyI.F.(Integrating…

Q: Show that the differential equation x¹y³ + x(1+y¹)y' = 0 is not exact, but becomes exact when…

A:

Q: 4. Obtain the Differential Equation from the family of curves of the form y = xC

A: To form a differential equation from given family of curves. Differentiate given family of curves…

Q: Show that given differential equation is not exact and hence find its general solution (x³ + y°)dx –…

A:

Q: Solve the Differential Equation using METHODS OF UNDETERMINED COEFFICIENT: y''+y'-3y=4sin2x

A:

Q: 2. y' + p(x)y = q(x)

A:

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.