z2 – x² – y2 = 1 %3D -

Q: y' + 2y = e*,

A: Note: Since you asked multiple questions, I solved first one if you want answer of other questions…

Q: Higher Order L.D.E (D2-2D+10)2y=0

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Q: y" + 2y' +y = e-*

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 6. S -3dy 2y2+14y+70

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Q: Find a particular solution, y,(x), of y(ª – y" = 12e3 – 5x + 2. -

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Q: (tVE2 + y² – y)dt + (y/E² + y² – t)dy = 0o %3D |

A: We will find out the required solution.

Q: xsin-1x > [4) S*s dx [4] S Y1-x2

A: Here is the solution

Q: 5T 1 y=-2cos(Gx+っ)+1

A: Phase shift: -5π

Q: rx dydx Vx2+y2 0.

A: We solve this double integration problem by substitution method as given below in solution

Q: y'' - 6y' + 9y = x^-2(e^3x) using Methods of Variation of Parameters

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Q: y² (y + 2)ï dy

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Q: xy = e2x; y 2х ху — е

A: We will find y' as following.

Q: y(2x³ -x²y + y³)dx – x(2x³ + y3 )dy = 0

A: y2x3-x2y+y3dx-x2x3+y3dy=0

Q: y'(t) = In(y- 3) %3D

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Q: 4. y(y² - 2x²) dx + x(2y² - x²)dy = 0 [Answer: x²y² (y² - x²) = = C

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Q: (D³– 4D°D'+ 5DD2 – 2D ) z = e'*2* + Vy + +2x +Vy +x. |

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Q: | d²y +y³ = 0 dx² is not linear. صواب İhi

A: True

Q: · (D² + 3D + 2)y = xsin 2x

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Q: find dy/dx

A: Known formula: ddx∫rxqxftdt=fqx q'x-frx r'x.

Q: f(x) = %3D 4 — т

A: We will approximate f(x) by the Taylor series. Taylor series of function fx at a is defined as:…

Q: ) y( 3x*- xy - 7)d -x ( xy ty- 2x) dgy = 0

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Q: y"'-3y"+2y'=t+et

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Q: د؟ لر ول 3 y3 Xe dydx

A: We have to integrate the function fx, y=x3ey3 within the given limits of integration but the…

Q: y" - 2y' + 2y = e'cscx

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Q: 6. x = t and y = 3t – 2 for 0Sts4 %3D -

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Q: +2x (D³ – 4D’D'+ 5DD" - 2D") z=e** + Vy +x.

A: Given PDE is D3-4D2D'+5DD'2-2D'3z=ey+2x+y+x We can write it as D-D'2D-2D'z=ey+2x+y+x             (1)…

Q: y" + a1(x)y = 4 sec²(8x)

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Q: = / y ²³. (X²+1) (3x+4) 5/ (2x-3)(x²-4) Find dy da

A: To find dydx:

Q: dx xy dy x² + y² Ans. y² = 2x²ln (

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Q: 1. y" - y' - 2y = e* %D

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Q: 2 da x² – 8x + 17 Integrate: + C

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Q: dydx x² +y²

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Q: 1l y" + 4y' + 4y = e-2x %3D x2

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Q: y(a² + y² )dx – x(x² – y² )dy = 0 %3D

A: Given: yx2+y2dx-xx2-y2dy=0

Q: + d²z Oy2 = 0;

A:

Q: Н. W.: -1/3 6dx 2. V9x2+ 1 c2/3 dy

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: y= x^4-3x^2+4x-3 find derivativr

A:

Q: (у-3) dy y2-6y+1

A: To evaluate the integral: ∫(y-3)y2-6y+1dy Solution: ∫(y-3)y2-6y+1dy…

Q: ydx + 2(y4-x)dy=0

A:

Q: Vy² – 25 dy y3

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

Q: f(x) = v2x2 – 13 s %3D -

A:

Q: 2d²y -X dx² dx +y=(b+1)(b +2)x(In(x))

A: Given : x2d2ydx2-xdydx+y=b+1b+2xlnxb This is homogeneous linear diff. eq.

Q: 4. xy+2x D /y

A: Solution:Given xy+2x =yTo differentiate explicitly with respect to x.Formula:(uv)'=uv'+u'v

Q: dy y2+1

A:

Q: Y1 (x) = 8a + 2x; y2(x) = x In(bx); y3(x) = ca?.

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Q: dy 6. S: y3-2y2

A:

Q: y² (y + 2)ã dy

A:

Q: V8 -x² 2 (x² +y²) dydx

A:

Q: Q = - ST 8-x²-y² x² + y² y dz dx dy

A: