Find the particular solution of 9 d2x d'y dy 122 + 4y = 3x - 1 given that when x=0, y=0 and %3D dx dy 4 dx 3 II

Q: dy x +1 xy %3D dx

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Q: The particular solution of y(x+y)dx + (x +2y- 1)dy=0; y(0) = 2 by NEDE is

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Q: Solve the particular solution of the given DE: x(r^3-xy^2+2y^3 )dy-y(r^3+2y^3 )dx=D0 @r=1, y=1.

A: We have to solve given problem:

Q: Obtain the particular solution of the DE: 4(3x + y – 2) dx – (3x + y) dy = 0; when x = 1, y = 0…

A: Gg

Q: Reduce the given DE into Bernoulli's equation: - 2x*y¬ dx 3 y-4 dy_ y5 2x4 y4 dy dx dx 3 3 dy 2x* у…

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Q: 3 dx – dy = o; y(o) = 6 x² dx + y² dy = o; y(9) = -1 x dx + 2y dy = 0; y(1) = 2 4 cos 2u du – e5v dv…

A: As per our guidelines we are supposed to answer only 3 sub-parts of a question

Q: Find the General and Particular solution of dy/dx = 4y ; y = 3, when x = 0

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Q: Solve the homogeneous DE 3xy dx + (x^2 + y^2) dy = 0.

A: We will take the substitution y=vx, to convert it into separable variable form.

Q: A particular solution of 4x² dy dx dy 4 is vx +8.x- +y = de

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Q: obtain the general solution.  dx =t(1+t2)sec2xdt. (1+In x)dx+(1 +In y)dy =0

A: (1). The given differential equation is: dx=t1+t2sec2x dt

Q: (b) Integrate: () S(4x3 — Зх? + 2х — 1)dx 3 (ii) - S-o S,(2.xy + z)dx dy dz z=-1 Jy=0 Jx=1 dy du =…

A: Solution:-

Q: Show that y2 +x – 3 = 0 is an implicit solution to dx dy on 2y the interval -o to 3

A: To show that  y2+x-3=0...(1) is an implicit solution to dydx=-12y on the interval (-∞,3)

Q: ) Obtain the particular solution of (2x-3y+4)dx+3(x–1)dy =0; when x =-1, y = 2 O Find the general…

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Q: Solve for the given DE: y(y^3-x)dx+x(y^3+x)dy=0

A: first we will check this is exact or not this is not exact then we will find its integrating factor…

Q: I. FIND THE GENERAL SOLUTION OF THE FOI dy dy = xy + 3x - 3x dx 1. dx

A: As per our guidelines we are supposed to answer only one question

Q: dy (=)y = x* sin x. dx

A: Linear differential equation

Q: 3X An integrating factor for the DE dy + ydx = e³*dx 5 O ey O y O ex O x?

A: For a differential equation of the form, , the integrating factor is defined by .

Q: The integrating factor of dx dy 2 y= 3x² is а. b. 1 x С. d. 1

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Q: y_x + y х х — 1 dx

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Q: Consider the following. 2y dx — х dy %3D 2 dx dy Solve for dx dy dx Is y 3x2 + 1 a solution to 2y dx…

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Q: Find an integrating factor for the DE y(4x – 3y – 3) dx +x(x- 2y – 1) dy=0_

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Q: Find the particular solution to DE:  ( xy^2 - x ) dx - ( 2x^2y - 3y ) dy = 0 ; y ( 1 ) = 2

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Q: If y = f(x) is the solution of (5aty – 12a – 2y³)dx + (x³ + 4y³ – 6xy?)dy = 0, f(0) = 0, then

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Q: 5. Find the particular solution (IVP) for the DE below: a) dx +2 =8x when x = 2, y = 6 b) 3y2 = 2x +…

A: Use variable separable method

Q: The solution of dy/dx = y2 with initial value y (0) = 1 bounded in the interval %3D

A: Introduction :

Q: I. Find the general solution of the following: dy 2x 1.- dx y dy 2. xy dx 3. dy = (6e3x+ 1)dx

A: We have to find the general solution.     According to our guidelines we can do only one question so…

Q: Find the Complete or Particular solution OF the Followoilng diffi rential equations: (2メコ+ )dx -2メよ…

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Q: - d² y dt² y (0) = 10 dy 4 - 5y = e-3t sin(4t); y (0) = 3, dt

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Q: 1. Show that the solution of: dy x? y 1.1 with initial condition , y(1) = 2 dx 1+ x3 is y = V4 +…

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Q: dx · xcot2y = x³csc2y dy

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Q: Find the general solution of the DE dy/dx = y(x – y) / x^2

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Q: Solve the general Solution of:  (xsiny/x- ycosy/xdx)dx + xcosy/x dy=0

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Q: dy 2) Find implicitly: dx (a) xy+3x2 =y? (b) exy – Iny =x? %3D

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Q: dy _ 2y = x-'y¯1 y(1)= 3 dx

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Q: Show that the DE (4y3 -6xy)dy = (3y2 +2x)dx is exact and find a solution of the IVP: (4y3 - 6xy)dy…

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Q: The Integrating Factor for the DE y dx = (ye' – 2x)dy %3D is: -2y レマ None of These 2y

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Q: Zy dx = (x?-1)L dx-dy) %3D

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Q: Find the general solution of the DE (x + y)dx + (x - y)dy =0.

A: Given differential equation is(x+y)dx+(x-y)dy=0Here, M=x+y and N=x-ythen ∂M∂y=1 and…

Q: Let y(x) be the solution of the IVP dy - (y - 3)'dx = 0, y(0)=2. Evaluate y(13).

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Q: dr2 dx dx d²y, 7 dy , 9y 3. dr2 dy =1 at x = 1. dx = 0; y = 0 and x dx x2 4. Use the method of…

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Q: From an integral equation corresponding to the diffrential equation d'y +x + y = 0 with the initial…

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Q: Derive the general solution of dy 1. dx y

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Q: Use RK Method of fourth-order to solve equation dy/dx = 1+y2 for x = 0.2 and x = 0.4 with h = 0.2.…

A: Given differential equation is                  dydx=1+y2 with initial condition   x=0, y=0 To solve…

Q: Solve the Euler equation d²y dx dy -5y = 0 dx 31 d', 3x2 given that y(1) =1 and y'(1) = 2. intai

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Q: d*y 2) Obtain a particular solution for d²y dy + dx + y = x3 + 2x +1 dx4 dx?

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Q: Find the general solution of the ODE. d'y dy +3. dx² dx Stre

A: Given d2ydx2+3dydx=5x+xex

Q: Find the general solution to: dy d dx dy 1 dy Cos x + sin 2x dx x + 4 dx

A: d). Given differential equation is dydx=cosx+sin2x. Re-writing the given differential equation.…

Q: Find the particular solution of (2x²y² + xy' )dx + 3 y? dy 0 that satisfies the condition y=1 when…

A: To solve the following differential equation

Q: Find the general solution to the following DE. y +x² dy = 0 dx

A: Given DE, y2+x2dydx=0

Q: The particular solution of y(x+ y)dx + (x+ 2y- 1)dy=0; y(0)= 2 by NEDE is

A: Let's find.

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.