Verify that the general solution satisfies the differential equation. Then, find the particular solution that satisfies the initial condition. See Example -10x general solution y = Ce differential equation у'+ 10у %3D 0 initial condition y = 6 when x = 0 y =

Q: Form the differential equation by eliminating arbitary constant :y=ax3 +bx2

A: We have to eliminate arbitrary constant a and b by differenciation

Q: Show complete solution Differential Equation: ydx-xdy=y^2dy

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

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Q: Find the general solution of the differential equation or state that the differential equation is…

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Q: D4 − 1)y = 0 -

A: Topic:- solution of differential equations

Q: Make up a 2nd order differential equation that you feel confident possesses only the trivial…

A: To find- Make up a 2nd order differential equation that you feel confident possesses only the…

Q: What is a separable differential equation? How do yousolve it?

A: In a separable differential equation, we separate the variables and then take the integration of…

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: Form the differential equation by eliminating arbitary constant :y=ax3+bx2

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

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

A: Given that

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

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Q: The equation y" + y'- 2y = x² is called a differential equation because it involves an unknown…

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Q: Suppose that a fourth order differential equation has a solution y = -3e5Isin(z). Find the initial…

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Q: Find the solution of the differential equation that satisfies the given initial condition. 2yev'y' –…

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Q: Reduce the differential equation: x2(y-px)=yp2 to chairaut form and find its genenral solution

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Q: y"″ − 3y" − 4y' + 12y = 0 -

A: To find the general solution of the differential equation y'''-3y''-4y'+12y=0

Q: (y – c,)² + (x – c2)² = 1 %3D -

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Q: 4. (D* – 1)y = 0

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Q: What will be the order of the differential equation if its solution is y=Acos7x-Bsin7x

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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: 4. eª y – ye" 2xy?

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Q: -3-x+x. y (0) -2. y(0)

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Q: yu) + 2y"+ y - x²sinx

A: The given differential equation is: y(4)+2y''+y=x2sin x

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

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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: Which are the differential equations and initial conditions?

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Q: Determine whether the statement "The function y = 0 is always a solution of a differential equation…

A: Here the given statement is The function y=0 is always a solution of a differential…

Q: A solution which contains as many as arbitrary constants as the order of differential equation is…

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Q: give an own differential equation     solve for the solution when  x=2 and y=0

A: Given, We have to write own differential equation  and Write the particular solution when x = 2  and…

Q: Find the general solution for the differential equation

A: Given: The given differential equation is X'=45-26X

Q: Solve the differential equation ry"+2(1 – x) y' + (x – 2) y = 2e", if yı = e² is known as a solution…

A: given differential equation  xy''+21-xy'+x-2y=2ex                    ...i claim- if y1=ex is a…

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

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Q: Describe the difference between the general solution and a particular solution of a differential…

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Q: Vyy" – 1 = y'

A: Given DE is  √(yy''-1) = y'' ......(1)

Q: If m1, m2 are the real and equal roots of the auxilary equation of second order linear differential…

A: Let us consider the second order differential equation y''+py'+qy=0 To solve the differential…

Q: Find the solution of the differential equation that satisfies the given initial condition.

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Q: Find all solutions to the differential equation y '= −5y. Which solution satisfies the initial…

A: Given: 1. 2.  Initial Condition To Find:  All the solutions of the given Differential equation.…

Q: Make up a differential equation that does not possess any real solutions.

A: A differential equation consists of a dependent variable, independent variable and derivatives of…

Q: 3. (D² + 4)y = 0

A: Given:         D2+4y=0      Auxiliary equation is        m2+4=0         m2=-4          m=±-4…

Q: Show that, if y, is a solution to a differential equation of the form y"+P(x)y' + Q(x)y = 0, then, a…

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Q: Verify that the general solution satisfies the differential equation. Then find the particular…

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Q: 21

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Q: Solve the differential equation ry" +2 (1- x) y'+(x- 2) y = 2e", if y1 = e" is known as a solution…

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Q: 2 11 y+xy+y%3D45inlnx

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Q: If the general solution of the differential equation having 7 arbitrary constants, then the order of…

A: Explained below

Q: If the general solution of the differential equation having 20 arbitrary constants, then the order…

A: Given: A differential equation having 20 arbitrary constant. Concept Used: Number of arbitrary…

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: Find the general solution of the differential equation or state that the differential equation is…

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Q: When is an equation considered as a solution of  differential equation?

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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.