15. Prove: If a, b, c, a, and M are constants and M = 0 then ax²y" + bxy' + cy has a particular solution yp = Axa (A = = Mxa constant) if and only if aa (a − 1) + ba + c ‡ 0.

Q: 23. Find the standard form of the equation. 81x -162x +36y² – 144y – 2691=0 (x-1)° , (v– 2)* - 1 [A]…

A:

Q: 5. The quadratic equation x² + ax+b=0 has two roots a-3 and b-3, where ab 0. What is a + b?

A: For a quadratic equation, ax2+bx+c=0 sum of roots=-ba product of roots=ca

Q: As x→4, k(x)→ As x→−10, k(x)→

A: Given a graph for various values of x and y. We need to find: As x→4, k(x)→ As x→−10, k(x)→

Q: 3. An organization deteremines that the cost per person of chartering a bus is given by the formula:…

A:

Q: 9. The general solution of x' = -6 -4 x is: 2 | ++(-:)| (a) x = Cịe-2t + Cze¬2t (b) x = Cye" () +…

A:

Q: 5. The equation 12x = 20 has 4 solutions in Z56. In general, the number of solutions in Zm to the…

A:

Q: independent solutions of y''+ P(x)y'+ Q(x)y = 0. Assume that f1(x) has at

A:

Q: 6 - Show that x(t) = (C1 + C2t) e¬t is a valid solution to i + 2yi + 7²x = 0.

A:

Q: Write in factored form. Determine the x-intercepts. y = x². - 1

A:

Q: 3. (a) Cardamo and Ferrari discovered that to depress a cubic, it is sufficient to let x = y − the…

A:

Q: Let (x, y,) be the solution of the following equations In 2 (2x) = (3y)m3 3Inx: = 2Iny Then is

A: This is very complicated & lengthy problem.So I can do it in Advanced Mathematics.

Q: 6. Find the general solution to: y" – 2y + y = x²e"

A: