Solve the given differential equation. dy - 4x² +3y° 2xy- dx

Q: Solve the differential equation as follows: 8x(x² + 3xy + y-)dx + (28x³ + 5x*y¬1 + 6x²y¬2 + 6y¯2) dy…

A: Given that, 8xx2+3xy+y-1dx+28x3+5x4y-1+6x2y-2+6y-32dy=0 Let, M=8x3+24x2y+8xy-1 and…

Q: Identify the type of the equation dy y? - dx and solve it.

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Q: If we measure time in hours the differential equation in part (b) changes. What is the new…

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Q: dy 3х + у dx = x +3y, dt %3D dt

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Q: Find the general solution of the differential equation y" + 2y' + 5y = e" sin 2x + a?

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Q: y dx x dy + = 0 /1-3 ln x I|

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Q: 1. Solve the differential equation d²y dx2 dy 4. + 13y = e2x dx For which y = 1 when x = 0 dx

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Q: 3. у" + 6у' + 8y — Зе 2л + 2x + 2х

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Q: dx x3 3x². -8(y + 1) = 0 dy y+1

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Q: d?y 2.3 -- y = 5e2x, with y(0) = 0 and y'(0) = 1 dx2

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Q: Solve the given exact differential equation:  (Please write clearly so i can follow the steps)…

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Q: dy dx = x+1 2(y+3)

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Q: 4. Solve the differential equation 2x(2x – 1) - (x + 1)2 + y = 0 using the method of Frobenius. dx2…

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Q: Solve the given differential equations: dy 1. 2+y² dx

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Q: 2 メy e

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Q: Solve the given differential equation. All solutions should be found. dy ° – 6y NOTE: Use c for the…

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Q: dy xy (differential equation) 2. Find the complete solution of the differential equation dx Vxty – y

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Q: 1. Find the general solution of (sin y – 2xcos²y)dx + x cos y(2x sin y + 1)dy =

A: Follow next step

Q: Consider the following higher-order differential equation. y(4) + y" + y" = 0 Find all the roots of…

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Q: (ycosx + 2xe') + (sinx + x²e° – 1) = 0 dx

A: We have to solve the following differential equation -  ycosx+2xey+sinx+x2ey-1dydx=0

Q: 5. x'dy-y°dx= xydy

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Q: 7. dy - yCot x dx = tan? x dx ; y = 2 when x = %3D

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Q: dx ussydy; y = sin 3X sinsy coS3 X

A: Given:- Sin(3x) sin(5y) dx= -cos(3x) cos(5y) dy  y(π/4) =π/2 To find:- Particular solution of given…

Q: Solve the differential equation with the appropriate method. Finalize the answer equated to ky^n 2.…

A: We have given a differential equation ,  dydx + y = y2 sinx This is Bernoulli equation of the form ,…

Q: 4. Solve the given equation and discuss the family of solution dy/dx = (x-y)/(x+3y)

A: We will find out the required solution.

Q: Find the solutions of the following differential equation: y²e2x dx - (4 + e2*) dy = 0.

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Q: Show that the given differential equation is exact and find the general solution. (2y'e* +3x? )dx +…

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Q: Solve the differential equation by variation of parameters. y"+ y = sec(0) tan(0)

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Q: (1+ siny)e*dx + (1+ e*)cosy dy = 0 ; y(0) = " 4

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Q: yy = 5æ³ sin(x) + y5

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Q: Vx sin Jy y' = (1 – VI)³ %3D

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Q: sin 3X Sinsy dx = - cos3X ussydy; y@=

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Q: 9. xdy +(y+x'y² ) dx = 0

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Q: dy y =2+ 2x + 1 dx 1. Find the general solution of х y = x(2x + In x + C) у %3 х(2х + хln x + C)…

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Q: solve the following differential equation. 9x +y-9 dx

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Q: 2. [x – y5 In(2y) x²]dy + ydx = 0

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Q: xy²dy = (y³ – x³)dx

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Q: e' y"-2y'+y= 1+x

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Q: Solve the following ODE. 2*y" = 2ry' + (y')°. (3/)°.

A: Consider the problem x2y''=2xy'+y'2let y'=uso, the equation…

Q: y" + 4y = 4 cos x + 3 sin x – 8

A: For particular integral of cos ax or sin ax we put       -a^2 in place of D^2 in F(D)

Q: d²y 4+y = 2e3*cosx 2.2 dx² dx

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Q: 2..3 dy x'y dx sec x ||

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Q: Solve each of the following differential equations. Find the explicit solution. d²x dx dt 2. cost…

A: Differential equations are those equations of mathematics that involve dependent variables ,…

Q: Find the differential equation of the given general solution by eliminating the arbitrary constant.…

A: Let us consider the general solution of the form f(x,y,c1,c2,.....)=0 To obtain the differential…

Q: 7. y' = csc x - y cotx

A: The given differential equation is; y'=cscx - y cotx.

Q: y dy = x(1 + x²)1/2(1 + y?)!/2 dx %3D

A: We need to solve D.E.

Q: 3 21 X y Y'

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Q: Solve the given differential equations:

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Q: 2. Find the particular solutions of the differential equation indicated below. (y - Vx2 – y³)dx –…

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Q: Find the differential equation of the given general solution by eliminating the arbitrary constant.…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.