Without solving the given initial value problem find the possible largest interval for its solution S ry" – x²y' + y = In (1 – In z) y (4) = 2 A) (0, 00) B) (0, 1) C) (e-1, e) D) (0, e) E) Ø

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

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Q: Find the general solution to y" + 7y' + 12y = 6e*. %3D

A: Consider the provided question, y''+7y'+12y=6e-xAuxilary equation…

Q: 8) Solve the initial value problem: y' = 5e +9x²- 7x y(0)=9

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Q: Compute r"(t). r(t) = + (5t³)j + (4 ln(8t))i

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Q: FIND 2 DIFFERENT (LINEARLY IN DE PENDËNT ) SOLUTION S POR THE D.E y"_x² y'- 3 xy = O *y'-3xy%3D0

A: Step:-1 Given that y''-x2y'-3xy=0 ---(1) This is second order differential equation with variable…

Q: y' x+1 y" + + e²y = 2³ + == y(5)= 1, y'(5) = 2. ithout solving the IVP, determine the longest…

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Q: Write the Taylor series for f(x) = e* about x = 4 as • Σ cn (x − 4)". n=0 Find the first five…

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Q: N'+y'- -3y= 3t n-3y +2y

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Q: 17. Derive A) f(x) = 10x* –- 32x + e² %3D B) y = e-* sin x

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Q: Which of the following is a solution to x'=A(t) x + b (t) if a) v (t) = b) O v (t) = v (t) = d) ○ v…

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Q: 5) Give a particular solution for y" – 2y' + y = 1+x2

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Q: A right trianglewith dimensions of X = 3 cm and y =4cm.if Cx) is increasing at arate of 2 cml sec…

A: We will find the rate of change in z

Q: 33. The solution of the differential equation +Py=Q where P and Q are the function of x is a) y =…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: The differential equation for the family of curves y = Cx – 4 is 2y + 8 %3D ху Find the family of…

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Q: Find a particular solution to y" + 6y' + 9y = 3z e

A: We use the method of variation of parameters to find the particular solution to the given…

Q: If M(3) -1 and h'(1) = 5, then h"(x)dr = (A)-6 (B) 4 (C) 5 (D) 6 (E) 9 (F) 11 Oc OF OD OE O A OB

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Q: f(x) = Co = C1 C₂ C3 = || = C4 = Represent the function 21n(9-x) as a power series (Maclaurin…

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Q: Solve y' -y = y*e* A) y(c - x) = e", y = 0 8) y(c - x) = 0, y = 0 Cy = e, y = 0 D) y(e - x) = e", y…

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Q: x(1 - 2х)у" - 2(2 + х)у + 8у%3 0

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Q: b) The charge q in an electrical circuit is given by d²q dq 1 +R+79 = E . If inductance L is 0.25 H,…

A: The solution is given below

Q: If y1 and y2 two solutions of (1 – a²)y" – 2xy' + n(n+1)y = 0; -1<x < 1 Show that W (y1, Y2) : 1-…

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Q: 2) Find a general solution for y" + 8y + 16y 0 then find the particular solution for which y(0) = 1…

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Q: H.W (3) 1-f(t)=te"; 2-f(t)=3+t² + cos2t. 4-f(t)=e¹.t³. 3-f(t)=e" sin 3t; 5-f(t) = (2t+3e²¹ +4sin…

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Q: a, b, c, d

A: Hello, thanks for the question. Since we only answer up to 3 sub-parts, we’ll answer the first 3.…

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.