Given that x = 3 is a solution to 2tx - y = 4, what is the value of 12t - 2y?

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Q: If the general solution of (2x2 – 3y2)y' = 2xy is y“ Iny*| + xª Cy“, what is the value of b? A 1 2…

A: The given equation is; (2x2-3y2)y'=2xy.

Q: When solving Jx² + 4y? = 16 Lx² - y? = 1 %3D by the addition method, we obtain y² = 3, so the…

A: Given that, x2+4y2=16x2-y2=1 And solution is y2=3

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Q: Find the general solution of x (z? – y?) +y (x² – z?) = z (y² – x) Z. a y

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Q: What is the general solution to: y''' - 4y'' = 0

A: Given y"'-4y''=0

Q: (D² + D)y =x+| ;

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Q: Using your answer to the previous problem, find the general solution to the problem a?y" + xy + (x²…

A: To solve the given differential equation we use method of variation of perameter to find particular…

Q: Find the solution to   x′=y y′=12x+4y   if x(0)=0 and y(0)=5.

A: we have to solve system of differential equations

Q: 6x +5_ 5(2 – x) %3D 2 3

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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: у" + 2y' +y = 4e' ¬x

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Q: Show by direct substitution that is a solution of y" +xy=0_ _and write the general solution.

A: Given that, y=xj1323x12 And the given differential equation is, y''+xy=0...1 The solving by power…

Q: dy = 6x(y – 1)2/3. dr

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Q: Solve the equations below for x, if pos 3x-1 a. %3D 4. 11 b. 6 – 5(2x – 3) = 4x + 7 %3D 3x c. + 2 =…

A: The general rules for solving equations for x are: i) simplification of each sides of the equation…

Q: (2) z?y" – ry + y = 4x lnx

A: Given DE is x2y''-xy'+y=4xln(x)......(1) We solve this DE.

Q: r²y" + 3ry' + y = In(z)+1 z((In(z))²+1)

A: The given differential equation x2y''+3xy'+y=ln(x)+1x((ln(x))2+1) is a homogeneous linear equation.…

Q: Find the general solution of the following: 7. (D³ – 4D² + 4D)y = 0

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Q: y' +?y = 8x

A: Solved below

Q: tind the general Solution of the different ial equation! PxLx-2)-Pl2yー2xyーX42)+y+リ=0 +ソ=。

A: Find the general solution of the ODE:xx-2p2-2y-2xy-x+2p+y2+y=0

Q: (ху+ усotx)dy — у(хdу+ ydx) 30

A: Given the differential equation             (xy+ycotx)dy-y(xdy+ydx)=0

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Q: To determine if y(x) = e-3* is a solution of y" + 3 y' = 4y , the first step is to find O y O y'(x)…

A: Given that y(x) = e-3x .is a solution of y" +3y' = 4y . We find first step and y"(x) value. Here i…

Q: Given another equation x- y = 2 2.2.1 Put x = 0 and solve fory

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Q: What is the solution of the DE: x²dy + y²dx = 0? A. x+y = cxy C. -=c x y B. D. None of A, B, or C -…

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Q: given the equation ; x²y" + 2xy' – 2y = x y(1) = 1 ve y'(1) = 0 solve with the conditions.

A: consider y=xm differentiate  y'=mxm-1y''=mm-1xm-2 substitute the values in given differential…

Q: Find the general solution of the following: 1. (4D2 – 4D + 1)y = 0 %3|

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Q: The particular solution to y" + 2y' + y = x is: Select one: а. 2х-2 b. 2х- 1 С. d. X- 2

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Q: What is the value of C of the solution to y' - 3y = 6 given y(0) = 5? O-2 3 O-3

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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: Find the general solution Ans. y=(C1+C2x)eX+e*

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Q: What is the particular solution if y(1)=0? 1/2 xy = y + (x² + y³)"

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Q: what is the privet Solution to the equation (0'+0)y(x)=Xsinc) (X)

A: The given differential equation is D3+Dy(x)=xsin x The particular integral of vsin x , where v is…

Q: The solution of y – 6y – 2y = 0 is -

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Q: Show by direct substitution that is a solution of y" +xy=0 and write the general solution.

A: Given :

Q: Find the solution of ydx = 2 (x + y) dy 2x + y = Ca² O z - 2y = Cy? O æ + 2y = Cy? 2a – y = Ca?

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Q: What is the solution to y' +2 = xy3? * +c a. b. = -x +c c. xy? = - +c d. xy = -x² + c e. None of the…

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Q: Solve the equation below for y. ons 3x + 2y = 4 %3D O y = -r + 4 O y = -0+2 Ov = +4 O y = -3x + 4

A: The objective is to find the value of y.

Q: Solve the general solution 3x² ydx + (y* - x*) dy = 0

A: Solved below

Q: Given that y(1) = 1 and y'(1) = −1, find the solution to x2y'' + 2xy' −2y = 2x2.

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Q: what would be the best way to solve the formula to get x by itself.  ex. y=7x-2kx. Im stuck with…

A: To solve for any variable which occurs in more than one spot is to apply basic mathematical…

Q: Find the general solution y" + 3y + 2y = 3e-t cost + 4e

A: To find the general solution of the given differential equation

Q: Given that where a > b solve for x in terms of a and b: b(x + 5) > ax + 8b

A: An inequality is an expression involving the symbols ≤,≥,>,< . It is used to compare two…

Q: Find the general solution of the following: 6. (4D² – 4D + 1)y = 0 %3| -

A: Please refer the attached image for complete solution. THANK YOU.

Q: The particular solution to y" + 2y'+y =x is: Select one: a. 2 O b. 2x - 2 O C. х - 2 d. 2x - 1

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Q: set up the appropriate form of a particular solution yp, but do not determine the values of the…

A: Consider the provided differential equation, y5-y3=ex+2x2-5 Set up the appropriate form of a…

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.