Given that yı e" is a solution of ry" + (1 – 2x)y' +(z - 1)y=0, find its second solution y2 on (0, o0), which %3D is linearly independent from y1- xe O (* - 1)e O e * In z eIn r Oe Inz

Q: C1 and C2 are arbitrary constants. Note: Y1(t) 2t and y2(t) = e2t are independent solutions of y" –…

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Q: Determine by substitution if y(x) =xe* is a solution of y"- 2y' +y = 0 %3D

A: Given  The differential equation is y''-2y'+y=0

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A: We find whether the given statements are true or false.

Q: d a value of r> 0 such that h(z) = z² +22³ + z + 1 has all its zeroes in D,(0).

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Q: Find the explicit solution of dy/dx=2xy² + 3x²y², y ( 1) = − 1 O 1/y=3-x²-x3 Oy=x²/2+x²³/3-3…

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Q: Įsin x cos^(3/2) x dx * O -2/5 cos^(5/2) x + C O None of the choices -5/2 cos^(5/2) x + C O -2…

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Q: Let y1, Y2 be two independent solutions of (t – 1)y" – ty' +y = 0. If W(y1, Y2)(2) = e² , then W…

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Q: If y₁ and y2 are linearly independent solutions of t2y" + 4y + (5 + t)y = 0 and if W(y₁, y2)(1) = 5,…

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Q: Give a particular solution for y" – 2y' + y = 3e*.

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Q: D) (3x² – 2y + e*+Y)dx + (e**y – 2x + 4)dy = 0 (Exact) E) (2xy*e" + 2xy³ + y)dx + (x²y*e" –x²y² –…

A: Let us consider the differential equation of the form Mdx+Ndy=0 The equation is exact if ∂M∂y=∂N∂x…

Q: Suppose that z'y"+ azy' + by = 0 has the general solution of the following form: y = C23 + C,r³ In…

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Q: e a. y; = +e-2= In(e" +1) +e-* In(e" + 1) – 6 2 b. Y, = re2" + e In(1 + e") – e2" In(1+ e") C. Y; =…

A: Option (a) is correct.   See the solution in the attachment.

Q: Verify by substitution that y(t) = Cekt - b/k is a solution ofy '(t) = ky + b, for real numbers b…

A: The given differential equation is y't=ky+b and the function is yt=Cekt-bk

Q: = In z are two linearly indepen- of ry" + y' = 0, then the partic- - ry" + y' = f(x) can be written…

A: We have to choose the correct answer from the given options according to the given condition

Q: 1. Verify that y = e²x + 3xe²x is a solution of the ODE y" - 4y + 4y = 0. (Show all work when…

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Q: 3 L[y] =y' --y is a linear operator. If u(x) = −4x² + 2x, then find L[u(x)]. X a) -4x² - 6x b) -…

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Q: Y, = Ax² is particular solution of y' + y" = 1 for A = %3D

A: Here, yp=Ax2yp'=2Axyp''=2Ayp'''=0

Q: Find the general solution of dy/dx = (x - 4) / (6 - 5x + x^2). O y = 2 In(x - 2) - In (x - 3) + C y…

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Q: If y₁ and y₂ are linearly independent solutions of ty" + 3y'+te^5t y = 0 and if W(y1 y2)(1)= 3, find…

A: and  are two linearly independent solution of

Q: If y, and y, are linearly independent solutions of ty" + 3y' + tey = 0 and if W(y,, y2)(1) = 6, find…

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Q: Find the solution of z'y" + bay + (4 + 4r)y - 0, z > 0 of the form where co 1 Enter n1,2,3,...

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Q: Obtain two linearly independent solutions valid near x = 0 x(1-x)y" - 3y' + 2y = 0

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Q: 5. Find the general solution of (D³-D)y=4e*+3ex. Ans. y=2xe*+(1/2)e2+c1+c2e*+c3e*

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