Which of the following functions are solutions of the DE y-4ry 0? (a) y 5z2 (b) y= e2 (c) y=3e1 (d) y = 3e2 %3D

Q: If y is a function of x, then the equation (y – )dx +3ry dy = 0 is not • but both + and + with n=…

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Q: Q1. Solve the following dy (a). y² + xy³ + (5y² – xy + y³ sin y) = 0. %3| dx

A: Let's find.

Q: Which of the following is the particular solution to the DE y(9x – 2y)dx – x(6x – y)dy = 0; y(1) =…

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Q: dy/dx = (xy + y^2 + x^2)/(x^2) Finfd the solution of the above equation using a suitable…

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Q: 3. Determine the general solution. a) y"–2y' – 3y= e* b) y"+9y= cos x

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Q: 6. (2x + 3y)dx + -x)dy 0 %3D

A: Consider the given equation as 2x+3ydx+y-xdy=0

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A: This is homogeneous ordinary first order nonlinear differential equation

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Q: Consider the following IVP: y"-3y'+2y = e*; y(0) = 0, y'(0) = 0 Find the general solution.

A: We solve the given DE  y"-3y'+2y=e3t.......(1) y(0)=y'(0)=0......(2)

Q: If y is a function of x, then the equation (y – a)dx + 3ry²dy O is not + but both and with n= After…

A: This question is related to diffential equation.

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Q: 1.) (2x + y + 6) dx + (2x + y) dy = 0

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Q: Solve the following ODE using the method of variation of parameters y" – 4y' + 4y = (x + 1)e²*

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Q: Determine the Solution of the following D.E.: (2) xydx + 2(x2 +2y²)dy D0; when x=0, y= 1

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Q: Q5) Answer the Following: 1- Solve the separable DE: dy -x² dx y² A a gortain

A: Given differential equation : dydx=-x2y2

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A: Given that: (x2+36)dydx=1        and  y(6)=0

Q: Find the general solution using substitution of the following DE: 1.) (2x + y + 6) dx + (2x + y) dy…

A: To Determine: Find the general solution using substitution of the following DE:

Q: Find the solution of the D.E. xydx - (x2 + 3y?) dy = 0 Show your solutions on a separate sheet of…

A: Given differential equation is xydx - (x2 + 3y2)dy = 0

Q: Find the general solution of dy/dx =(1+y^2)e^x. Write your solution y, as a function of x.

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Q: Find the solution of the D.E. xydx - (x? + 3y) dy = 0 Show your solutions on a separate sheet of…

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A: consider the program min 12x1-52+12x2-52              ...i such that 0≤x1≤20≤x2≤2 claim- to solve…

Q: Q2: find the general solution: (D* - DD')z = (x² – 2y)e" + sin (2x – y) •2

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Q: dy Solve the initial-value problem for y as a function of x. (x? +9) - = 1, y(3) = 0 dx

A: Given(x2+9)dydx =1 ⇒dy =dx(x2+9)

Q: Find the Particular solution of the ODE d?y dy -6--7y = -9e-2x, dx2 at y(0) = -2 and y(0) = -13 %3D…

A: We have to find the particular solution of the ODE                       d2ydx2-6dydx-7y=-9e-2x at…

Q: Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx b.…

A: Separable equation:   A first order differential equation y’ = f (x, y) is called a separable…

Q: Q16// find the general solution (cosx)y²dx + 2ysinx dy = 0

A: I

Q: Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx = x* +…

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Q: 22/ Solve two of the following D.E- dy + 4 +4y =0 A) dy B) di+2d3 - 3y=6 undetermined coeff.]

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Q: dy Solve the initial-value problem for y as a function of 2. (64 – x²) - 1, y(0) = 6 dr y =

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Q: Which of the following functions y is a solution :of the DE (1-x)y"+xy'-y=D0 ? Select one А. e2х В.…

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Q: Which of the following functions is a solution of dx 12x – 8y dt dy 16x – 4y | dt

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Q: III. Find the particular solution of each of the following. dx 1. dy 2x - 7y*; when y=1,x=-1

A: Find the particular solution of each of the following. dxdy+2xy=7y4; when y=1, x=-1

Q: H.W. Solve the O.D.E メ+5y u sing 5X° ys homogenos ogenous methd

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Q: Show that the equation Əy + 2k Əx? possesses solutions of the form 00 2 c, e-kt 1" =0 Σ cos (a, x +…

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Q: Find the solution of the following ODE: dy 1- dx y = 0, y(0) = 1 1+x2

A: Linear differential equation is of the form dydx+Py=Q Where, P and Q are continuous function of 'x'…

Q: (10) Solve the given BVP by using Green's function: ; (ii) y" – y/ = e2; y(0) = 0, y(1) = 0

A: Given differential equation is: y''-y'=e2x y(0)=0y(1)=0 Green function in equation is given by:…

Q: dy Find the solution of the Bernoulli's equation x + 6y = 3xy4/3. dx 1 1 а. у b. y (x2+cx)3 (x+c)3 1…

A: We solve by Bernoulli's equation.

Q: Solve the initial value problem for y as a function of x. dy (x² + 196) 23, у(14)%3D 0 dx %3D The…

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Q: Find the general solution of the given ODE: dy x²y-4y dx x+2

A: The solution of the given differential equation is  y=e(x22-2x+C)or y=Ce(x22-2x)

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Q: II. Solve the following first order DE. (x² + y²)dx + xy dy = 0 4.

A: Explanation of the solution is given below...

Q: Q3: Solve the following equation using Runge Kutta Method to for the range 1.0(0.1) 1.5 , given that…

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Q: Solve the following initial value problem for y as a function of x. dy x = /x? - 16, 3x dx x24, y(4)…

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Q: If y = f(x) is the solution of (-12ay+ 2x)dx + (-4x³ – 48y?)dy = 0, f(0) = -1, then %3D Lütfen…

A: The equation is exact so we can solve directly

Q: (D³+3D²– 4D)y = 0 -4x Question 5 Find the solution. dy 31+9y=2ty 5/3 dt

A: P

Q: Which of the following is a solution to xy' + y + x*y*e* = 0 ?

A: The solution of a differential equation is defined as the function that satisfies the differential…

Q: Solve the non-homo . D.E. 1.y" + у %3D Зе2х

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Q: dz dz and Suppose z is a function of æ and y, and tan Vy² + x² = z#e6y. Solve for

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Q: 5. Which of the following functions are solutions of the DE y-4ry = 0? (a) y = 5a2 (b) y = e2 (c) y…

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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.