Let y, = e*, y2 = xe* be two independent solutions of y" - 2y' + y = 0 ,x > 0 then the particular solution for the ex non homogeneous equation y" – 2y' +y = is 1+x2 Y(x) = %3D A. -; e* In (1 + x²) + xe* tan x B. - In (1+ x²) + tan x C. ex + xe* D. Ce* + C2xe*

Q: 3) Find dy dx a) y = x+In(sec 3x) %3D In(x+)

A: solution:-

Q: 7. Given y =x*in*, calculate y'. sinx sinx A) y'=xin* (sin.x Inx + cos x Inx) C) y'=x*inx + cos x…

A: For the solution of the problem follow the next step.

Q: The characteristic equation for a 5th​ degree, homogeneous, constant coefficient DE is​…

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Q: dy B) Find for all the following dx 1) y = sin-13x 2) y = In(5x) 3) y = Vtanhx

A: Solution: As per our guideline we are supposed to answer only first three question please repost…

Q: y"-3y" + 3y'-y = e²

A: Solution is uploaded in the image in scanned form.

Q: tan²xdx = sin³ydy when x = 2, y = 3

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Q: i) tanzy dy sin3xdx

A: As we know that  (i)  tan2y=sec2y-1(ii) ∫sec2ydy=tany+C(iii) sin3x=3sinx-sin3x4(iv)…

Q: find dy/dx y = | Vx V 1 5) 1+x 20) y=Cof"| 1-x, 15) y = \tan /2x + 7

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Q: Euder-Caue

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Q: 7) (1+x')dy + 2xydx = 0

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Q: (4) M" - afg' -4fg= 0; Y@-1, g'()=0

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Q: Find the solution of ordinary differentral equation X+2xy'-2y=L4xlox -5cos(Inx)

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

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Q: Find y' in y=sin¹ (5x5+2x) + Tan-¹ (x²) 1 1 1+x² -(5x5+2x)² A. y' B. y' C. y' D. y' = = 25x¹+2…

A: Given:y=sin-1(5x5+2x)+tan-1(x2)       y'=dydx=dsin-1(5x5+2x)+tan-1(x2)dx…

Q: dy if 6 + sin 2y = dx 2y + 3x by using implicit differentiation. 2y + 3x Find Hence, find the…

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Q: What is the integrating factor of (1 + cos x) y' = sin x (sin x + sin xcosx sin x 0 1 + cos x CSC X…

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Q: Find dy/dx for the following : 9) y* = sin-1 x %3D 10) y = xtanx + sin-ly 11) (Vy)* = (In…

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Q: 4. Find the general solution to the DE 2x²y + xy'-3y=0.given that y₁=- is solution.

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Q: 2xdx – [3y* +(x² - y' )tan y] = 0

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Q: 2) (3x²y+ 4e)dx + (x³ + 4xe + 2y)dy

A: We are authorized to solve only 1 question, please repost remaining questions Differential equation

Q: Are these equation separable 1.s2+ds/dt = (s+1)/st 2.dr= b(cosx dr+ rsinxdx) 3.y'=ye(x+y)/(x2+2)

A: The objective of the problem is to determine whether the given equations are separable. A…

Q: Obtain the general solution using variation of parameters (D²+3D+2)y=cos(e^-x)

A: We have to solve the given differential equation by variation of parame

Q: c) f(x)=tan(cos².x) 11 COS X 1+ sin.x Dy=- b) y = 2

A: e)  f(x)=tan(cos2x)  f) y=cosx/(1+sinx) g) y=ex^2/x3 Repost the next part.

Q: 4. (sin y - y sin x) dx + (cos x +x cos y- y) dy = 0

A: Note: As per our guidelines we are allowed to solve one question

Q: Find the largest interval on which the LV.P (x +(4) x -5) y" + sin(x) y' + y =0, y(0)= 3, y'(0)=4…

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Q: -7x f(x, y) = e" sin(4x + 5y) af e^(-7x)(4cos(4x+5y))-7sin(4x+5y) af 5e^(-7x)cos(4x+5y) dy ||

A: Partially differentiate with respect to x and y by using product rule.

Q: Let y(x) be the solution for the DE y+ytan(x) + sin(x) 0 If y(0) = In 2, then at x= the value of y…

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Q: 4) x²y + xy² + xy = -1 ,y' at x = -1 %3D

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Q: guess the form of the solutions 1- y’’ - 2y’ -3y = 3sin(5t)+tcos(5t)+2te^-t 2- y’’+2y+10y=4te^-t-…

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Q: 2) (y+1)dx+(4x- y)dy =0

A: According to our guidelines, we can answer only the first problem or three subparts of a problem,…

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.