(d) P(X + Y = 4),

Q: Is y = e-x + 2xe-* a solution to y" + 2y' + y = 0.

A:

Q: d²y Find dx2 , if y vx-x Jy = 9

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Q: d²y - y = у 3 10sin?x %3| dx2

A:

Q: dy ニ 3 x +y-2

A:

Q: S Sz(x² + y³)dxdy, wherein B = {(x, y) E R²; 0 < x² + y² <4}.

A: Double integral

Q: Find the general solution of using the method of variation of parameters. d²y dy 2- - 42+ 2y = xe 2x…

A: Given,2y"-4y'+2y=xe2xComplementary SolutionAuxiliary Equation is 2m2-4m+2=0⇒m2-2m+1=0⇒m-12=0⇒m= 1 ,…

Q: D={(x,y):4 < x² +y² < 81,< x <-V3y}, V3 Find [S, dA JJp y2

A: We will use polar co ordinates to solve the problem

Q: Find d2y/dx2 in terms of x and y. x2 + y2 = 3

A:

Q: dy If y = esr+11 then- dx 8e8x+11

A: If function is efx,  then its derivative is f'x efx

Q: · (D² + 3D + 2)y = xsin 2x

A:

Q: Obtain the general solution. 1. y' = xy?

A: We will find out the required general solution.

Q: d3y find 3 5) If y = 4x + z %3D dx3

A: Given that: y=4x3+3x2

Q: Find d2y/dx2 for the equation x=x3y2-3y3

A:

Q: Find d2y/dx2 implicitly in terms of x and y.

A: To findd2ydx2

Q: The general solution of the DE: -y = 1 is y= x(x + c)

A: given,1xy'-1x2y=1multiplying throughout by x we gety'-1xy=xnow, integrating factor μ(x) is given…

Q: Solve for A y and dy if y = f (x) = -3x + 2x2 – 3x +5 %3D and

A: Given that: y=f(x)  =-3x3+2x2-3x+5

Q: Solve for d2y/dx2 for x = u2 - 3 and y = 4u3 - 2u

A: Given x=u2-3 and y=4u3-2u. To find d2ydx2. Solution: We have, x=u2-3 Differentiating the given…

Q: Find the General and Particular solution of = 3y ; y= 3,when x = dx

A:

Q: nd the general solution to: 2yy -e^ = 0, |

A: The question is taken from the calculus in which we have to find  the general solution of  given…

Q: Find the general solution using variation of parameters. - 4y + 4y = (x + 1)e²-

A: To solve the following problem

Q: d'y dy y = aebx is a solution of %3D dx2

A:

Q: Find d2y/dx2 implicitly in terms of x and y. x2y − 3x = 8   d2y/dx2 =

A: Consider the given function, x2y-3x=8 use implicit differentiation method and differentiate with…

Q: 3. y = x³ – 3(x² + w²) 4. y = x7 + V7x - 1 TT + 1

A: Differentiation wrt x

Q: -4x e Find a particular solution to y" + 8y' + 16y= x3

A:

Q: The f ²-3)³ dx is equal to x2

A: Given: I=∫x2-33x2dx For evaluating given integral, first we simplify given expression then integrate…

Q: - 19. y = cos TX, y= 4x² – 1

A: We have to sketch the region and find the area under the curve.   According to our guidelines we can…

Q: of dx forf = 3x² y² – 4.x³ y Q2. + -

A:

Q: Find the General and Particular solution of = 3y ; y = 3, when x = 0

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Q: 7. Find the general solution of (Dʻ + 2D’ + 10D²)y = 0.

A:

Q: dy Find dz given that y = -2 – 8z². z=-3

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Q: Obtain the general solution using variation of parameters. (D^2 − 1)y = e^x + 1

A:

Q: Qs) y" + 3y' + 2y = e* – 3

A: See the details solution in below

Q: Find the solution. dy x-+ 5y =2r2y4 dx

A:

Q: The y, of y'"-y=2x²-x -3 by using variation of parameters is: .A y,(x)=Ae*+ Be- .B Yp(x) = x – 1 .C…

A: Given that  y"-y=2x^2-x-3 To find the particular solution by using the variation of parameters

Q: b) f(x, y)=-2x². + 8x − 3y² + 24y + 7

A:

Q: If y = x3 – 2x2 + 3x – 1, then d2y/dx2 is equal to

A: topic - derivatives

Q: v x +y = 2xy + 4x; at x = 1 and y = 3

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: 4-y² ²) dædy 2 2

A:

Q: Q5: 6y²dx-x(2x² + y)dy == 0 (Linear BernoullLeq.)

A:

Q: What is the general solution of differantial equation?  Whicf of the options x² - y² + xy dy/dx =0

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Q: Vy² – 25 dy y3

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Solve the dff oq dy 3x寸票-5-2 %3D

A:

Q: if x3 + y3 =65, find the value of d2y/dx2 at the point (4,1)

A: Given that,    x3+y3=65

Q: f (x, y) = x² + 3y² + 4,

A: Supposing the question is asking to find the local minima value.

Q: d³y Find dx3 where y = e*(8x + 1)

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Q: dy y2+1

A:

Q: - (D² +2D+5)y=e* sin 2x

A:

Q: + Vs + es +- ds n = 3 From left endpoint s² + 1

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Q: Find S- y dy Vy+2 using the substitution u +5=√√y+2.

A:

Q: dx Vx²-4x-7 7. dy y2-8y+5

A: