If the general solution is \( y=c_1x^{-2}+c_2cos(2lnx)+c_3sin(2lnx), \) the Cauchy-Elera equation is Select one: a. x³y" + 5x²y" + 12xy' + 8y = 0 O b. x°y" + 6x?y" + 12xy' + 8y = 0 O c. x°y" + 2xy' + 8y = 0 С. O d. x°y" + 5x²y" + 7xy' + 8y = 0

Q: The characteristic equation associated with x" + 19x' - 27x = 0 is Select the correct response: m2 +…

A: Given:- x''+19x'-27x=0 To find :- Characteristic equation of given differential equation

Q: Solve the D.E.: (2xy - 3x^2) dx + (x^2 + y) dy = 0 Show your solutions on a separate sheet of paper.…

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Q: Q1) L-¹ (²-1) = a) cosht -1 Q2) The general solution of y"" + 2y" -y'-2y = 0, is: 2x a) y(x) = c₁e²x…

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Q: -1/2 6) xdy+ydx=(x²+y')"/?(xdy-ydx)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The solutions of cosh(2x) = 8sinhx - 5 are a) x = ln (4+ √17) and x = ln (1 + in (1 + √2) b) x = ln…

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Q: Solve if w be cube root of unity then (1+w)(1+w^2)(1+w^4)(1+w^8).....2nfactor=1

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Q: The integral 2a12 + 5x° is equal to -dx 3 x5 + x3 +1 (a) -25 + C (2) +2² + 1)* (b) z10 +C (1 + کے +…

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Q: 2. Solve X' - 3x – 4x+12 2 0 algebraically (number line)

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Q: 8. Find y'ifys34-7x+2)+4%-2

A: Differentiation

Q: If x, y belongs to Z prove that the equation x^2+4x-8y=11 has no solution

A: The given equation is, -----(1)

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 x and y. if (x y) (² _-3) = 4 -1 = (2-4).

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Q: 9. (a) 2 Find the maximum value of 3 cos²x-8 (b) -3 (c) -5 (d) -8

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Q: Find dz (3z4+4) 1 3a1-72+4 Option A Option B 36a° /E(3a1+4) (3r-4)* 3a -6r+4 -69r+4 VF(324+4) Option…

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Q: Q2: Solve 1- y// + y = secx

A: As per the company's guidelines, we are supposed to answer the first question for you, Kindly repost…

Q: 1. (r - x) + (-2r + 3x) 2. (-y + 3) - (v - 2) 3. (-3a* + 4 + 2a') -(2 + Sa - a) 4. -(6 - b + 4b')…

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Q: Find the general solution of the D.E. ye? dx = (4+e2") dy Show your solutions on a separate sheet of…

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Q: (2xy s) 10x*y Sx*y (-243x*yy

A: Due to our guidelines I am solving only first three parts plzz repost other question.  1. (2x5y3z)2…

Q: Trigo Substitution

A:

Q: The general solution of +y= 2, with y(0) = 0 i , O ye? = 3e? – 3 O None of the choices O ye? = 2ez +…

A: this is linear differential equation

Q: x3 – 2x? – 5 = 0, [1,4]

A: f(x) = x³ - 2 x ² - 5 , [1,4] f(1) = -6 <0,  f(2) = -5 <0, f(3) = 4 >0, f(4) = 27 >0…

Q: Find a general solution to the DE (D^2 + D- 6) y = 5e^2t by: a. Undetermined coefficients b.…

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Q: Please find the general solution of the following equations: (x - 1)3y''' + 2(x-1)2y'' - 4(x-1)y' +…

A: *By Bartleby policy I have to solve only first one as these are unrelated problems.These are…

Q: |(r +x² +x+1)(3x* +4x° + 6x² + 12x + 1) dx (x3

A: Use the substitution method and simplify the integration first then integrate.

Q: +√Y'+Y=X²² 15 10) SOLUTION TO THE GIVEN DE (4D²-8D²7D²+ 11 D+6) y = 13 11) solve the ff DE (D²+215³…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Explain the step by step process to get the final answer Problem #2: Differentiate f(x) = [(3x* –…

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Q: 2. Given that f is a differentiable function with f'(3) = -5, find g'(1) where g(x) = f(4x-x²)

A: The given function is,

Q: ii) y" - 3y'-4y = 2x2-3.

A:

Q: How do I explan that x2+4xy-Sin(y2) is not a quadratic form?

A: To justify that the given expression in x and y is not a quadratic form in x and y

Q: 1. Solve (D¹⁰ + 3D³ – 20D6 – 48Dª + 64D²)y = 0

A: As per guidelines, I can solve only first question ( Question 1)

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.