Which of the following equations can be reduced to the homogenuous linear differential equation with constant coefficient? O a. dy 32. da? da 0 = 32. 3 dy = 0 da3 da 3 dy 2 dy da? da? da O d. a d'y dy dy da? da O e. dy da2 da ||

Q: Apply the method of successive approximations to the initial value problem dy/dx = 4xy,  y(0) = 3,

A: The given differential equation is dydx=4xy, y0=3 We have applied the successive approximations.

Q: Determine whether it is stable or unstable. D) dx₁ dt = 3x₁x2-x1 + x2 dx₂ dt =x²-x₁

A: D Given system of differential equation is dx1dt=3x1x2−x1+x2dx2dt=x22−x1 We have to determine…

Q: dy Find the solution of 2ху + dx X. 2у-1

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Q: solve D.E. by using separable of variable dy 1 V2xy dx

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Q: Find the general solution of dy dr - 2 y + 1 x+y-2

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Q: 2. Solve the ff. equation using integrating factor. dy 2y – e3r dx

A: Given: dydx=2y-e3x

Q: Solve for the IF of the equation y(x + y + 1)dx + x(x + 3y + 2)dy = 0 OA. OB. ey eLny ALT OD.y

A: Given : yx+y+1dx+xx+3y+2dy=0 To Find : IF of Given equation

Q: dy Which is the of the equation y = e 2x +3? dx 2 В. х+ 3 С. 2х + 3 O x + 3 2X + 3 2e 2x+3 Option 4

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Q: (2y3 – x³)dx + 3xy?dy = 0; when x = 1, y = 1 Ans. 5x²y3 = x5 + 4

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Q: Which of the following equations is an exact DE? a. 2xy dx + (2 + x²) dy = 0 O b. x²y dy - y dx = 0…

A: To find Which of the given equations is an exact.

Q: Which of the following is linear equation? a. 3x + 2y-z² = 0 b. sin 2x + y = 1 c. log x + 2y = 2 ww…

A: The equations are To evaluate: The linear equation.

Q: 37. Solve the equation where a, b, c, and d are constants. dy dr ay+b cy + d'

A:

Q: 2 Find dyif y.+3x-7 and x =, 2t +1

A: As per our guidelines we are supposed to answer only one question.Since you have asked multiple…

Q: dy 4у dx х (у-3)

A: Given query is to find the soly of the differential equation.

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Given functions are: y=a2-t2x=42t2+a In order to calculate d2ydx2, firstly we will calculate d2ydt2…

Q: The equation y? = cx is a general equation of A. y' = 2 B. y = 2x 2x C. y' = y y D. y': 2y O A NONE…

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Q: ) y(4) +y" + y² + y = x³ + 2x + 1 Find the special solution to the following differential equations…

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Q: Differentiate. g(t) =  5 − 7t 8t + 9 g′(t) =

A: solution: the objective is to find the derivative of the given function

Q: SOLVE FOR dy. x dx Yo WHEN x = 0; y₁ = 0; C = Constant C - Yo - x kyo

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Q: . Find the general solution of dy d.x = 2 y + 1 x+y-2 2

A: Given differential equation isdy/dx = 2 ((y+1)/(x+y-2))2

Q: 2. Solve the DE: (2x + dx + 2y ) dy = 0 1+ x?y? 1+ x?y?

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Q: Find an equilibrium solution df/dx = 2f − 6. a. f = 2 b. f = 3 c. f = 4 d. f = 5

A: Given Data: Differential Equation: df/dx = 2f − 6 The equilibrium solution is the point where the…

Q: Solve using the differential operator D=d/dx. Use Method of Variation of Parameter [D2 - 8D + 16] y…

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Q: 3. Find dy of the following equations: dx a. y = |(e-3x² + 7x² + In 8x

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Q: Find an expression for dy/dx. y = u? and u = 3x - 1 18x 18x - 6 0 9x -3 O 6x - 3

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Q: Let y = 5x?. Find the change in y, Ay when x = 2 and Ax 0.3 Find the differential dy when a = 2 and…

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Q: p= I.F. = e/P(x) dx Now solve (I.F.) y = f (I.F.) - Q(x) dx 9. Solve the linear ODE using an…

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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.