If the quantities x and y are related by the equation y = 3x, then we say that y is to x and the constant of is 3.

Q: If y(x) is a solution of xy" +(1-x)y' +6y = 0, find the value of y'(2). %3D

A: Given differential equation is xy'' +1-xy'+6y=0 -----(1) Also,  y'' +1-xxy'+6xy=0 Here,  limx→0…

Q: It is easy to check that for any value of c, the function y = ce 2+e= is a solution of the equation…

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Q: dy X -2= y² - 3y dx

A: We use variable separable method to solve the given differential equation.

Q: Find the particular solution of xy" + xy' 13; y = 0 and y' = 1/2, when x = 1.

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Q: Find the particular solution of x²y" + xy' = 1; y = 0 and y'= 1/2, when x=1.

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Q: If x, y e R satisfy the equation x2+ y2 -4x-2y+5 0 and S (x + ry) then value of is 100

A: Given : x,y∈ℝ satisfies equation x2+y2-4x-2y+5=0 and S=∑r=099x+ry we want to calculate value of S100…

Q: ax + y + z 1 We will examine the solutions of the equation according to a. x + ay + % a x +y + az ||…

A: The given system is,ax+y+z=1x+ay+z=ax+y+az=a2

Q: The general solution to y'' - xy' + y = 0 is given by:

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Q: c) x’y'+ xy = 4y

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Q: Find the general solution for the given equation: y’’ + y = csc x

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Q: (6x + 1)(,F – 2) Suppose that y'(x) = and that y(4) - 3. Solve for y(x).

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Q: What is the solution of the given equation valid near the origin for x>0? x2y''+x(2+3x)y'-2y=0

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Q: An implicit general solution to the following equation (y/x^2)y'+ e^(2x^3+y^2) = 0, where y=y(x) can…

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Q: A. ELIMINATE THE ARBITRARY CONSTANT/S IN THE EQUATION. 1. y= Ae2x + Bxe2x 2. y = Ax² + Be¬* 3. y =…

A: Explanation of the answer is as follows

Q: ス g+y1(1-火)-x3.%

A: The given differential equation is y'+y1-x=x2-x It is linear differential equation of the form y'+px…

Q: The solution of (1 - y ^ 2) * d * x + (1 + x ^ 2) * d * y = 0

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Q: what is the general solution to the equation (o° +D)y (x) = x

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Q: Solve for the family of solutions of the following equations. 1. xydx + (x2 + y2)dy = 0 2.…

A: SOLUTION-

Q: Solve the following using variable separable. (y’)2 =  1 − y2/1 − x2         ;         y = 1/2, x…

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Q: What is the auxiliary equation for y"+by'+c=0, b & c is constant. What are the condition for this DE…

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Q: y' = 1+t – 2ty + y²

A: We have to check

Q: Verify if the indicated equation is an explicit or implicit solution of the given DE 1. y=csc(x+c):…

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Q: y"+ y= sec'r 4 sec*x %3D

A: We have to  find the  general solution of the given differential equation.

Q: Find the solution of y' + p(x) = 4x if y(0) = 3 and where

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Q: If the quantities x and y are related by the equation y = then we say that y is to x and the…

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Q: x' = -3x + 2y, y' = -3x + 4y; x (0) = 0, y(0) = 2 %3D %3D

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Q: Find the general solution of the equation y' +2xv = x and then find the particular solution y for…

A: Ko

Q: Find the general solution to the equation x²y" + xy' + y = 0.

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Q: Eliminate the arbitrary constants on the given equation: y= Ae" + Bre 2y +y=0 O y =-y" + 2g

A: The given equation is y=Aex+Bxex. We have to eliminate the arbitrary constants.

Q: Find the general solution of the equation: xy – y = x²e=x (x > 0)

A: find the general solution of the equation xy'-y = x2e-x (x>0)

Q: both

A: Put value of either x or y from equation 1 and put in equation 2 or value of either x and y from…

Q: x + y + z = 12 y – z + x = 6 Solve for a where a = x + y

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Q: The particular solution for the equation y' – 4y =x , y(1)=2 is Select one: 1 16 4x y = e** y = e*x…

A: Let's find.

Q: Observe that y = x is a particular solution of the equation %3D 2x²y" + xy' – y = 0 and find the…

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Q: (x*+ 2y)dx — хdу y' = csc x – ycot x

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Q: If e-x, xe-x are the solutions of y''+ay'+by=0 then, what are the values of a and b.

A: To find- If e-x, xe-x are the solutions of y'' + ay' + by = 0 then, what are the values of a and b.

Q: Now, we can set zy = 0, substitute 2x for y, and solve for x. + 21 = 0 = -21 X =

A: Substitution method: - The substitution technique could be a simple approach for determining linear…

Q: find a second independent solution of the given equation.…

A: Rewrite the given differential equation, in the form Divide the given differential equation with x2…

Q: Solve for the value of x : (1/2) *>(1/2)' y > x O b. x >y O c. y> 1/2 O d. x> 1/2

A: Given: 12x>12y

Q: Solve for x and y. x + yi = 3 e2j +4e-2j

A: Given complex number - x+iy = 3e2i+4e-2i             ...........(1)We know that,eiθ = cosθ+isinθ…

Q: We have determined that y = 1 and x = 52. Substituting these expressions into the third equation…

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Q: solve the given equation below: xy'=4y

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Q: y' + 4y = 3(e^2x)(y^2) , y(0) = 1, solve for y when x = 1, and solve for y when x = 1/2

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Q: Solve for x and y and determine if e 1 f 16x - 2 VDAS 4x+ 8y + 1 |12y-9 f 6.

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Q: Find the general solution of the following DE. xy² (y')² + y(x - 1)y' - x³ = 0

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Q: Show that the equation e^x = 1 − x has exactly one solution in R. Find this solution

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Q: (y–1)² ce-y. (z-3)5

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Q: 4. Eliminate the arbitrary constant on the given equation: y = x + C1e2 + Cze-20 %3D

A: The given equation,y=x+C1e2x+C2e-2x

Q: Find the solution to x' y – x +t y' if æ (0) = 2 and y(0) = 6. x(t) = help (formulas) y(t) = help…

A: Solution :-

Q: Find the general solution of the equation y' + ay = b a, b constants. a does not equal 0

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