1. Given y = 4e* + In x, find the differential dy.

Q: xydy – (y 3x2) dx = 0 –

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Q: For exact differential equation of the form Mdx + Ndy =0 %3D OA ay %3D В. Эх dy 0: D. ay

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Q: E. Solve tne differential Equotions ☺ Czxy + xln3x)dy + .(xtyJ dx =0 when x =3, y=2

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Q: What is the solution to the differential equation if x = 1 at t = 0 and, dx/ dt = 0 at t = O?

A: dxdt=0  at t = 0 means that the slope of normal line passing through the point (1, 0) is 0.

Q: b) Use Euler's method to obtain a numerical solution of the differential equation dy y = 4 - dx with…

A: given             y' = 4 - y/x     and y(1) = 3, we have to find

Q: Show that y = sin−1 x satisfies the differential equation y = sec ywith initial condition y(0) = 0.

A: The given differential equation is y' =  sec y,  with initial conditions y(0) = 0.We want to show…

Q: 1. Find the differential dy in y= 2x4-3x3-5x 2. Use differentials to find approximate values for…

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Q: on) solve the Differential en by using vanation of parameters - 24 (+12 yll -24¹ +y₁

A: Please see the below picture for detailed solution.

Q: Obtain the particular solution for the following set of differential equa dy = (4x2 + 7xy +2y²)dx;…

A: Given that: x2dy=(4x2+7xy+2y2)dx        and when x=2, y=0

Q: Find the particular integral of the differential equation belov (D² + 1) y = sec x tan x

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Q: Solve the differential equatons x(2y + In ax) dy + (x+y)dx when x=3 y=Ź y= 2 1.

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Q: An appropriate integrating factor µ(x) for the following differential equation (2y² + 3x)x+ 2xydy=0…

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Q: Solve for the particular solution of the following differential equUations. a. (x³ + 3y)dx –- xdy;…

A: The given differential equation is: x3+3ydx-x dy=0 ;    y(1)=3

Q: 4 If y = In(8+ x4), find the differential dy. Your answer will be in terms of x and dx. Enter dæ as…

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Q: Answer the following using Homogenous ODE in Differential Equation. 3xydx + (x² + y²)dy = 0

A: Hint: By putting y=vx we can solve homogeneous differential equation.

Q: What is the integrating factor to (2y2 + 3xy – 2y +6x) dx + x (x + 2y – 1) dy = 0, to make it an…

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Q: let (xev/x. y) dx – x dy=0 which is a homogeneous differential equation.

A: Given:

Q: Consider the differential equation dy (t – 81) + 5ty = sin(t) with y(1) = 2t. %3D There exists a…

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Q: Obtain the differential equation associated with the given primitive, A and B being arbitrary…

A: y=sinx+A y=sinxcosA+cosxsinA

Q: Suppose that x = 0 is a regular singular point of the differential equation 4xy" + 2y' + y = 0 Then,…

A: Given: x=0 is a regular singular point of differential equation 4xy''+2y'+y=0. To find: Indicial…

Q: solution of the following nonhomogeneous differential y" – 2y' +y = 4x² + e* %3D ned coefficients…

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Q: 5. Verify that y(x) = Vx+C is a solution of the differential dy dx 1 for every constant C. equation…

A: The differential equation is given as dydx=12y2ydy=1dx

Q: differentiate the following Differential equation x2(4xy+3y2-x)dx + x3(x+2y)dy =0 when x=2 , y=1

A: differentiate the following Differential equation x2(4xy+3y2-x)dx + x3(x+2y)dy =0 when x=2 , y=1

Q: 3. Plot the slope field for the differential equation = y² – x and sketch the solution for the…

A: Given: A differential equation dydx=y2-x. To sketch: Slope field of given differential equation and…

Q: 6) Solve the homogeneous differential x2 + y? dy quation dx 2xy

A: on solving this we get

Q: 1. Given that y satisfies the differential equation ,dy +22+y 0, use the approxinmations dx Yas -2y,…

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Q: Consider the differential equation x²y " – xy ' + y = 0. Given that y(1) = 2 and y '(1) = 3,…

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Q: Consider the following differential equation: (12xy3+32ysen(xy)cos(xy))dx+N(x, y)dy=0 Calculate N…

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Q: Obtain the general solution for the following differential equation using Separation of Variables…

A: Using method of seperation of variables

Q: For which value of k is the differential equation (x^k+y^k)dx + (2xy)dy = 0 becomes homogeneous?

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Q: If the differential equation corresponding to the family of curves y = (a + bx) e3x is given by dy =…

A: The given differential equation is d2ydx2=adydx+by....(1) Now, y=a+bxe3x is a solution to the…

Q: Find the general solution of the following second order differential equa d.x dt? dt

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Q: Show that any function of the form y = A sinh mx + B cosh  m x  satisfies the differential equation…

A: Given function y = A sinh mx + B cosh m x Differentiate the value function…

Q: 8. If y = xi, then the value of the differential dy as x changes from 16 to is (A) * (B) 5 (c) (D)…

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Q: 2. The exact differential d xdy - ydx what is the d(xe")= x?

A: Let's find.

Q: Write down a differential equation of the form = ay + b whose ay dt all other solutions diverge from…

A: We have to determine a differential equation of the form dydt=ay+b. The solution of differential…

Q: Q.4 Consider the differential equation (2y-2)y=2x-1.

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Q: 2. If y = find the differential dy. Hence, estimate the value of 1 + (1.023 1 +

A: topic- differentials

Q: 1. Construct a slope field for the differential equation = dy x + 2y dx

A: The given differential equation is: dydx=x+2y So the slope at any point (xo,yo) will be given by…

Q: 8. Compute the differential df of f(x,y) = log (x² + y²).

A: Given; f(x,y) = log(x2+ y2)

Q: Consider P(D)y = 0. What conditions on the rootsof the auxiliary equation would guarantee that…

A: Solution: Consider the given Differential Equation P(D)y = 0 Let the Auxiliary Equation of given DE…

Q: Show that the coefficients of the given differential equation are homogencous and solve the given…

A: Given, The differentiating equation  x2+2y2dxdy=xy   and  y-1=1 We have to show the coefficient of…

Q: Solve for the general solition of the followimg differential equation using FOLDE 2. (y - x + xy…

A: Given DE is  (y - x + xy cotx)dx + dy = 0.......(1) We solve this DE.

Q: Consider the nonhomogeneous differential equa 1 "(x) + y(x) = e '+ sin a

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Q: What is the appropriate integrating factor to the ff. linear differential equation? dy + (1+ xcotx)…

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Q: Find the function y: (0.x) → R that satisfies the ordinary differential equation ry'(x) + y(x) = x²…

A: Given : y : 0 , ∞→ℝ   ;  xy'(x)+y(x)=x2 cosx        ;  yπ = 0 To Find : solution of ordinary…

Q: 4.Find the particular integral of differential equation (D +2D]y =1+x².

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Q: Obtain the general solution of the given differential equation up to the form free from ln function.…

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.