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

A:

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

A: Differentiation

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

A:

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: 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: 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

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.