Compruebe que la ecuación diferencial - xy" + (1 − 2n)y' + xy = 0 Tiene la solución particular y(x) = x¹Jn (x)

Q: Find y as a function of a if y(0)2, y'(0) = 3, "(0) = -13. y(x) = y″ − 4y″ − y′ + 4y = 0,

A: Given a differential equation:initial conditions are:

Q: " Show that the substitution JAx + B| = 'e², or z = In |Ax + BỊ, will reduce the equation dy a(Ax +…

A: I have used the given substitutions to reduce the equation

Q: Use Exact, Then solve (1 = In(x) +)) = (1 – In(x))y`

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Q: Q/IF it was AY ₁2) = -12 Y(2) ℗ Y³ (2) = − 12 ⒸY² (2) = -11 Y³ (2) = -11 DÝ (2) = -13 © ²³ (2) = -13…

A: Given

Q: f(x + h) – f(x) f'(x) = lim h-0 %3D h bsnd Diffeentinble A) 7xh2 B) 9x2h C) 5x2 D) 9x2 5) Given (x")…

A: Given that: 4. f(x+h)-f(x)=9x2h+7xh2+5h35. (xα)'=αxα-1

Q: 2. Determine whether the functions f1(x) = e2", f2(x) = e=2#, and f3(x) = sinh 2x are linearly…

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Q: with y(0) -1

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Q: The auxiliary equation of  of  y'''-4y''-4y'+16y=0  is r^(3)-4r^(2)-4r+16=0  . The auxiliary…

A: Given that fr=r3-4r2-4r+16, r∈3,6

Q: Find y as a function of t if y(0) = 4, y(0) = 1. y(t): = 64y" - 144y + 81y = 0,

A: Given: The characteristics equation is             64m2-144m+81=0⇒m=--144±-1442-4· 64· 812·…

Q: If t²y" – ty – y = 0 ,y(1) = 3 and y'(1) = -1, then y(4) = . . . %3D

A: Given differential equation, t2y''-12ty'-y=0,y1=3,y'1=-1 Find the value of y4.

Q: a) If L-{F(s)} = f(t) and L-1{G(s)} = g(t), and if a and B are constants, then L-1{aF(s) + BG(s)} =…

A: If L[f(t)]=F(s), then f(t) is called the inverse Laplace transform of F(s). That is; f(t)=L-1[F(s)]

Q: Find y': y=V5+2 — 2 O y = 7-2x 2√5+2x-x² Oy = √2-2x 1 Oy = 2√5+2x-x² 1-x O y = √5+2x-x2

A: We have to find derivative of given function.

Q: Let f(u) = u* and g(x) =u = 2x* + 6. Find (fo g)'(- 1). (fo g)'(-1)= (Туре an exact answer.)

A: Given:- Let f(u) = u4 and g(x) = u = 2x4 + 6   To Find (fog)'(-1).

Q: Ex. 4) For F and G functions and given that: F(5) =-1,F'(5) =-3 G(5) = 4 G'(5) = 2 a) If P(x)= F(x)·…

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Q: If y = xsinx then prove that y''+y=2cosx

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Q: When you substitute y''p and yp into the equation, where does the: 4Ccos(2x) and -4Dsin(2x) come…

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Q: а.) Solve x' = -5] x+ -2 [sec t] x(0) 1 b.) Solve x' = x + x(0) 1 -2 U5

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Q: If x' x= [(-₁)] and x(0) = [] x what is X(T)?

A: Given: x'=01-10x and x(0)=01. To find: x(π)

Q: 8. Find all the roots of f(x) =x* - 4x' + 6x² – 4x+5 if 2-iis one root.

A: Topic- roots of polynomial

Q: 12. Find the second derivative for the function f (x)=4x+12x²-20x-18 and solve the equation f"(x)=0.…

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Q: Find y as a function of x if y(0) = 13, y' (0) = 22, y" (0) = 27. y(x) = y" - 15y" +56y' = 42e*,

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Q: Suppose that f(x + h) – f(x) = 7hx? – 8hx + 5h²x – 3h? – 7h³. Find f'(x).

A: The quotient difference formula is given as, f'x=limh→0fx+h-fxh it is given that…

Q: f(x) = sec x As x = π-/2, f(x) =  As x = π+/2, f(x) =

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Q: The function y1=ln x is a solution of xy''+y'=0 A) Find a second solution y2 on the interval…

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Q: 8. Find all the roots of f(x) = x' - 4x' +6x² – 4x+5 if 2– i is one root.

A: We will find all the remaining roots as following.

Q: Suppose X and Y are independent variables such that E[X] = 2, E[Y] = 3, E[X^2] = 9 and E[Y^2] = 15.…

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Q: 3) f (x) = 2 x2 + 4000/x +10 a)Find the derivative . b)Find the critical number(s), if any.

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Q: 3/(a) Let X × b(n, –) and E(x)= E(16–7x) find n.

A: Solution : Given : X ~ b( n, 14 )             E(x) = E( 16-7x ) To find n : It is known that for…

Q: Given f (x) = x³ - 3x – 1,x 2 2, find (f~')'(-1)

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