2) Let y = c,x + C,x ln x be the general solution to x'y" – xy' + y = 0 on(-∞,). Find c, and c, such that y(1) = 3, and y'(1) =-1.

Q: Let H(x) = F(G(x)) and J(x) = F(x)/G(x). Suppose F(4) = 9, F'(4) = -7 G(4) = 3, G'(4) = 0 G(-6) = 4,…

A: Given H(x)=F(G(x))H'(x)=G'(x)*F'(G(x))J(x)=F(x)G(x)J'(x)=G(x)F'(x)-F(x)G'(x)G2(x)

Q: The values of C, and C₂ so that y(x) = C₁x + C₂ (-) satisfies the two conditions y(1) = 1 and y'(1)…

A: Given: yx=C1x+C2-13x2 To find the values of C1 and C2 such that y1=1 and y'1=-1.

Q: - · x²y'' — 4xy' + 4y =12x4, y( 1) =1, y'( 1) =2 y( 1) =1, y'( 1) =2 Assume the values of x are (0,…

A:

Q: x²y" − x(x + 2)y' + (x + 2)y = 0, 0 < x

A:

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: Let F(x) = f(f(x)) and G(x) = (F(x))² and suppose that f(9) = 4, f(4) = 2, f'(4) = 8, f'(9) = 4 Find…

A: Given:   F(x) = f(f(x)) and G(x) = (F(x))2

Q: ,(x) = (x-x+1) y'(x)+3y'(x)+9 y(x) = 5x' +1 true false

A: False

Q: Obtain two linearly independent solutions valid near x = 0 x2y" + x(x-1)y' + (1-x)y = 0

A:

Q: find y(x) for x2y'-2xy=3x with y(1)=3

A: Given,         x2y'-2xy=3x  with y(1)=3

Q: titution: 4 11 8 }]ÿ. y(0) = [¯²]. etermined coefficients: 12 -1 · [¹² −¹5]y+[e²].

A:

Q: Obtain two linearly independent solutions valid near x = 0  xy" + x(x - 1)y' + (1 - x)y = 0

A:

Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using…

A:

Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+C₁e-ax using 2…

A:

Q: Solve: 2 0 -1 0 2 -6 1 -2 -3 -2 0 1 -5

A:

Q: 1. let y = x(x2+x)2  , Find y'   2. let f(x) = (5x)5 find f '(x)…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: f (x) You are given h(x) = f(g(x)); p(x) = f(x)·g(x); q(x) = g(x) and the following values f(2) = 1,…

A: Given : hx = fgxpx = fx·gxqx = fxgx

Q: b y' = 2 + ₁e-ax a

A: details steps are given in step 2

Q: Find the form of yp to use in the method of undetermined coefficients y"-3y'-4y=x²e*+xe* a.…

A: Our objective is given below:

Q: x(1 - 2х)у" - 2(2 + х)у + 8у%3 0

A:

Q: The general solution to: y'' – y' + 4y = 0 %3D is: y(x) = %3D Typle c_1 and c_2 to get c1 and c2 and…

A: We have to find the solution

Q: Let 2² + y? = 1 and y(0) = 1 Then y'(0)= none of the listed here 1 -1

A:

Q: 1) If h(a) = a + 1, find h-(x). (A) h-(x) = 3+ (x+ 2)3 (B) h-(x) = V – I (C) h-(x) = 2a3 – 3 %3D %3D…

A:

Q: | 1) Find a function y whose graph passes through the point (1, ) and satisfies x²y' = y.

A:

Q: Let F(x) = f(f(x)) and G(x) = (F(x))? and suppose that f(9) = 7, f(7) = 3, f'(7) = 14, f'(9) = 3…

A: topic - functions and derivatives

Q: x) such that f"(x)=2r' +3x-4

A: Integration: f''(x)=2x3+3x2-4x+5; f0=2, f1=0 ∫xndx=xn+1n+1+c

Q: 2x2y'' + 3xy' - y = 0 , x>0   y1(x)= x1/2 and y2(x)=x-1 Please verify that I have solution.

A: Differential equation.

Q: Determine the value of k such that y = 4x²_3e²r is a solution to x(1-x)y"+ (2x² − 1) y' + k (2x −…

A:

Q: Find the nonhomogeneous ODE whose general solution is y=c₁(x+1) ³+c₂(x+1)3³+x-1. (x + 1)² y" + (x +…

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: 1) If h(x) = x³ +1, find h-'(x). (A) h-'(x) = 3+ (x +2)³ (B) h-(x) = Vx – 1 (C) h-(x) = 2r³ – 3 (D)…

A: