(х + 2)3 y = (x² – 4)

Q: Find the particular solution for y' = x3 – 2xy when x = 0, y = 1

A: We are given a differential equation: dydx=x3-2xywith the initial cobdition x=0, y=1 We can solve…

Q: z2-ze coshw.K (z) z2– 2ze coshw.K+e2a -

A: The solution is given below. Hope this helps!

Q: %3D x2+7 X2 +7 to flx1-メ= LtzX as xI oc ニ I + 7/x?

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Q: 2. -1z"cosdz zl=1

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Q: -2xy 3) y' = iy = -5 when x = 2 Ans: exact; x²y + y = -25

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Q: Find the solution. xy'- xy = 1- y, y(1) = 0 A y --(1 - el-) © y -1+ el+")

A: Solution of the differential equation

Q: 7. x+y (2r +2y-x)' at (0, %) -4 at (-3y3. 1) 8.

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

Q: y= (2xy+ 3x²)ē+ (x² – 2yz + 2y)e, – (e² + y²)ē

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Q: y-y1=m(x-x1) y-(-1)=4/5(x-(-1)) y+1 = 4/5x + 4/5 y=

A: The given equation is y+1 = 4/5x+4/5      y = 4/5x+4/5-1         = 4/5x-1/5

Q: y''+2y'+y = x² Solve using D-Operator

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

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Q: 2r + 4 Solve R(x) 2 0, where R(x) X - 1

A: Replace the value of R(x)=2x+4x-1 in the inequality R(x)≥0. Then solve for x. After substituting the…

Q: xy = e2x; y 2х ху — е

A: We will find y' as following.

Q: -x-1 a) y' = +2yi-1 v(0)=1

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Q: Find a (real) general solution. y" + 2y' + 2y = 4e¯* sec³x

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Q: solve for y in terms of t or x, as appropriate.

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Q: · (D² + 3D + 2)y = xsin 2x

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Q: (2x+1)y' =e", with y(0)=0.

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Q: 10. (D² – 2D – 3)y = 0 when x = 0, y = 0, y' = -4

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

Q: 10--6A Oa) x- -6 V b) x = 6 c)x- 10 V d) x- -2 Oe) x- -8

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Q: x = 2 + 3t, y = cosh 3t , 0 <y<1

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Q: GiNen Y+ 3y -22 こ4 what is the value of - - マ+ メと 2y +3z = -1 X +y tz?

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Q: Solve for x and y. X = y = 17 1 5x + 20 5 [723]-[2725231 2y 1

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Q: Solve for Z. X= (Y-Z) 3

A: Given: X=23Y-Z We have to solve for Z.

Q: 2(x-1) + If y = Vx? – 2x then y' 3x2-2x T O F

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Q: If y = sech (kxN) and (1-289 x26 ) (y')² = A Then A =.....

A: We know ddxsech-1x=-1x1-x2 By chain rule ddxsech-1f(x)=-f'(x)f(x)1-{f(x)}2

Q: z = 6x + y2 tan 4

A:

Q: e²–3¤ /1 – y² given that wher

A: Given that, dy/dx = e^(2 - 3x) . sqrt (1 - y^2) Then we get, dy/[sqrt (1 - y^2)] = e^(2 - 3x) dx…

Q: -x+y+2z = -3 3x- y+z = -2 2х- Зу- 42 %3D 1 X = y =

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Q: in yy = 2 y-x; %3D

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Q: $] Solve y"-3y' = 2e* +5sin 2.x

A: We  have to solve the differential equation   y''-3y'=2e3x+5sin2xHere the homogeneous part  is…

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: Solve y"-4y'+13y= yo)=-I ,y'co)=2

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Q: y''-3y+2y=5e^3x,y1=e^x

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Q: Find the particular solution 3у %3 х3 — 2ху; when x %3D1, у %3D1. = x 2xy; when x = 1, y = 1.

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Q: (4) (y² +4)xpq-2=0 b z=alnx+-tan tan¹+c 2 2

A: Let us consider a PDE of the from F(x,y,z,p,q)=0 Using charpits formula…

Q: Solve []=[ x (t) = y(t) = - 3 1 -41 -5 [2] x(0) = - 2, y(0) = 23

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Q: y = 2z3 [tan(3z+1)] a + xy – y5 = 8x? y = (x + 3)² (x² – 2)

A: You didn't mention what should I do with the given equations and this problem is posted as calculus.…

Q: 19 -e 8x + · -2x y = c¡e¬* + c2e¯ xe8x %3D 8100 90

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Q: 4. Solve y 3x 3y + 2y" e using undetermined coefficient. Show all the work.

A: We need to solve D.E.

Q: - 2r2- 6y = -2x + 5y %3D he previous step at x = -3.

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Q: (D - 2D + 4)y = 0 ; y= - 2, Dy = 8, D²y = 0, when x = 0.

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Q: 2.3 - y 5e2, with y(0) = 0 and y'(0) = 1 %3D

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Q: 1 y = [cosh(2x)] co* ot-1

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Q: (xy^2 - x^3) + (yx^2 - y) y' = 0, y(0) = 1, solve for y when x = 2

A: Exact differential equation problems

Q: (D + 3D + 2)y = xsin 2x

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Q: 3 1 (x + 2y)dydx -1 a) 5 b)7 O d)-:

A: Please check step 2 for solution.

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

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Q: Express (2xy + 2x – 1) – (x² – y² – 2y)i in terms of z & Z then simplify.

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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.