Find the value of b, if a = 6, so that the general solution of this ordinary differential equation has as elementary solutions: [y1=1; y2=x^14

Q: Show that the given differential equation is not exact hence solve it 2²ydx – (2³ + y³)dy = 0

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Q: Find a suitable form for particular solution of the differential equation y5) + 25y3) = 5 – tešt +…

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Q: Using an appropriate substitution, solve the differential equation zdy/dz + y = 1/y²

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Q: Find the general solution of the differential equation. y′ = arctan x/ 2

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Q: solve the first order of differential equation dy/dx = y2 -4 using seperable method

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

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Q: What is the differential equation obtained by eliminating the parameter A from the relation…

A: The explanation of answer as follows

Q: Obtain the general solution of the given differential equation: tanydy = sin3xdx

A: The given differential equations tan2y dy=sin3x dx⇒sec2y-1 dy=143sinx-sin3x dx    As…

Q: Find the complete solution of the differential equation, y' = 2 - cot.

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Q: Solve the given differential equation using indeterminate coefficients y''' - 6y'' = 3 - cosx

A: The given differential equation is y'''-6y''=3-cosx. Its auxiliary equation is m3-6m2=0. Solve it as…

Q: y = Ae* + Be-*

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Q: Solve the given differential equation by finding an appropriate integrating factor to make it exact…

A: Given equation is the linear equation  of the form  dxdy+xP(y) = Q(y)  and integrating factor is…

Q: Solve the given differential equation by separation of variables. ds kS dr

A: We want to solve given differential equation

Q: Determine the general solution of the given differential equation

A: Rewrite the equation in standard form. And solve it

Q: Q1 By eliminating the constants A and B from the equation y = Asin 2x + B cos2x, form an ordinary…

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Q: Find the solution to the differential equation dx 8xy which passes through the point (0,e). Express…

A: We will solve the equation by method od separation of variables.

Q: Solve the given differential equation by undermined coefficients ya) – 5y" + 4y = 2 cosh x – 6.

A: By Bartleby policy I have to solve only first one as these are unrelated & lengthy…

Q: The independent variable x is missing in the given differential equation. Proceed as in Example 2…

A: Given:y+8yιι =yι2   →1Let yι =u →Ad2ydx2=dydxd2ydx2=dudy=dydxd2ydx2= ududy →Busing Aand B in 1we…

Q: the given differential equation is not exact and hence show that Solve it x²ydx -lx3+y?)dy=0

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Q: Solve the given differential equation by separation of variables. ds = kS dr %3D

A: dSdr=kS

Q: y= 4 + Inx; xy'

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Solve the given differential equation by separation of variables. dy = sin(3x) dx

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Q: Find a differential equation whose general solution is y = cie" + cze *. = 0

A: To find a differential equation whose general solution is given by, y=c1e7t+c2e−3t

Q: Determine the form of a particular solution yp(x) for the differential equation:   (c) y'' + 4y =…

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Q: Find the solution to the differential equation   that passes through the origin.   z=

A: As the solution function to the given differential equation, passes through the origin we will have:…

Q: Find the solution of the following differential equation using appropriate method.

A: Here we will find out the required solution.

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

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Q: If we use the method of undetermined coefficients, the particular solution of the following…

A: Using variation of parameter we know the standard form of the given particular solution.

Q: y(4) – 16y" = e¯* + sin3x y

A: find complementary function and particular integral and add them

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

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Q: Use the method of undetermined coefficients to find a particular solution to the differential…

A: Explanation of the answer is as follows

Q: Find the general solution of the differential equation using any method          y′ = √( 1 − cos )

A: Find the generla solution of given differential equation y'=1- cos x

Q: Write down a linear homogenous differential equation (with the smallest order and constant…

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Q: Given, (+) dz + (41) dy =i0 an exact differential equation. Az+1 Determine the value of A.

A: This question is related to exact differential equations, we will solve it using the condition for…

Q: Find the general/particular solution of the given differential equation:

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: Without solving for the undetermined coefficients, the correct form of a particular solution of the…

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Q: By the alimination of the arbitary constants a and b ,obtain the differential equation of which…

A: Given solution is xy=aex+be-x+x2 find DE by eliminating arbitrary constants

Q: Solve the given Cauchy-Euler differential equation. For problems with initial values, plot the graph…

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Q: find the Integrating Factor and Get the General solution of the given differential equation

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Q: Solve the given differential equation by separation of variables. dy = sin(6x)

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Q: 4. x" +x=e+!.

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Q: Solve the following 2nd order differential equation by Varition of parameters method. (D2 + 9) y =…

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Q: Find the solution to the differential equation dz 2te12 dt that passes through the origin.

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Q: Find the special solution of ele differential equation. = 20x - 4x3 dy dx y with the initial value…

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Q: y'tanxsin2y = sin²x + cos²y

A: Assume t=cos2y then differentiate both side with respect to x to find dtdx .…

Q: If we use the method of undetermined coefficients, the particular solution of the following…

A: y(5)+y(3)=x+cos(x) Particular solution : As equivalent function containing x so (To maximum order to…

Q: Verify if the given functions are solutions of the differential equation. Also, determine the value…

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Q: Use the method of variation of parameters to find the general solution of the given differential…

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Q: y"-4y = 0; cosh 2.x, sinh 2x

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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.