Compute the general solution valid near the origin ((+4x² )y" - By = O 'y= s{1 - 4x°) + a»\x= 22kx2k+1 k=1 4k2 – 1 (-1)**'22kx2k+1 °y=aol1 + 4x°) + as x + y=ag{1=4x°) + a;[x* Z; 4k? – 1 "r (-1)*22kx2k+1 4k? – 1 224, 24 +1 y=a,(1+4x?) +ax- 4k2 -1

Q: II Find the y"'of 3x-7 1) y = 2x+11 2) y= 6x-5

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Q: In (*-") l+V1-x2

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Q: Find y' where y = tan(11a? + 8) v173 + 17 Answer: 51a2 y/ = sec2 (22æ)\/172³ + 17+ tan(11a² + 8)…

A: I have used the rule for composition of function and multiplication of functions

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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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A: First lets put the values of theta in the equation

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A: Given differential equation is xydx−x2+3y2dy=0....1. We have to find the solution of the given…

Q: The general solution for the equation y'=x*e(x^2+y) can be given in the form of: ?ex^2+2e-y=k a) x…

A: Solve by separable variable method

Q: Find the number of roots of the equation z^4+4z-1=0 in the annulus 1/3<|z|<2.

A: Rouche's Theorem : If f(z) and g(z) are two analytic functions within and on a simple closed curve C…

Q: find dy/dx 4x -x 2x 23) y= Sin- +x².Sec 2-x + 2x.Sec) 2 (ans.: (2-2»N(2-x² - x* 4 4

A: To find the dy/dx means y' of the given function

Q: Solve for the general solution of the given DE: O y = (-6 + ce^(-x^2/4))^2 O y = (-6 +…

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Q: The solution of the IVP, y' = -2xy, y(0) = 2, is: %3D

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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: Eliminate the arbitrary constants A and B in the equation y = Acos5x + Bsin5x. O A.y" - 25y = 0 O…

A: Solution :  Options (B) is correct

Q: The equation (tan²x+3y²)sec²xdx + (3tan²x + y²)dy=0 can be solved by

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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: Find y': ○ 4kx (2kx + 1)7 ○ 4k (2kx + 1)7 ○ 8k(kx² + 1)7 ○ 8kx(kx² + 1)7 y = 1/(kx² + 1)8 ; k…

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Q: general

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Q: äbäi 14 Q) Find dy/dx of the following :equation (x' +x)(x° - x +1) y = 17 KB/S dy/dx = - 4/x^2 O…

A: We use the Quotient Rule and  Product Rule of differentiation to find the answer of the given…

Q: а) у%3DIn(x? + 4)(2х + 5) b) у%3DIn (12х - 7) с) у ex2+3 ex-4 - d) y= 2x'ex e) y = ev3x+T

A: Given data:   a) The given function is: y=ln(x2+4)(2x+5).   The expression for derivative of the…

Q: Solve z" + 2z" – 4z' – 8z = 0 -

A: We solve this question by simple techniques used to solve homogeneous differntial equation

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