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: =y"' + (x − 253 of the form 2 a2 with a = 1.1 powers, then Jak where f(k)= k=0

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Q: 1) 9y" – 30y' + 25y = 0 2) y" – 4y' + 3y = 0

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Q: Show that general solution of the second-order difference equation: ya+2 - Gyk+1 + 8yk = 2+ 3.k –…

A: Solve the second-order difference equation:                      yk+2-6yk+1+8yk=2+3k2-5.3k Find the…

Q: 3. [io 0| 2 0 1 0 -1 0 0 0 4 A. No solutions B. Unique solution: x = 2, y = -1, z = 0 C. Unique…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

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

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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: Which of the following is solution of (p - xy)(p – x²)(p – y²) = 0 (a) 3x - y3 - c = 0 b) xy + cy +…

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Q: Q4) A-Determine the particular solution of the equation y"-y=0 for yo-=0, yo'= -2

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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:…

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Q: Let (xp, y,) be the solution of the following equations In 2 (2x)™² = (3y)n3 3Inx = 2lny %3D Then xo

A: Given equations are 2xln2=3yln33lnx=2lny

Q: (b) Show that general solution of the second-order difference equation: yk+2 - Gyk+1 + 8yr = 2+ 3.k²…

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

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Q: Which of the following is a general solution to the following: x²y" + xy' + (36x² − 1) y = 0 A. y =…

A: Solution:

Q: 5. If Z1 = V3 – 2i, Z2 = -i+1 and Z3 = 4i – 2. Evaluate (i) Re{3Z} – 5Z7 + 2Z}} (ii) |(1+ Z2+ Z3)(i…

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Q: If the general solution of (2+²-3y2) y'= 2xyżsy"In|y"+xª = Cy", what is the value of b? (A) 3 B 2 -1…

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Q: Let (x, Y,) be the solution of the following equations (2x)" = (3y)m3 3Inx = 2lny In 2 %3| %3D Then…

A: Introduction :

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

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Q: Find the general solution to y = c₁e¹¹ + c₂e(8-√³)² + cze(8+√7)₁ Oy=c₁e¹¹ + c₂e³ + c3e-81 Ⓒy=c₁e¹ +…

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Q: 22. (MULTIPLE CHOICE) Which of the following statements is(are) true? (A) y = e is a solution of the…

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

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

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Q: Q2) n(x) = x1 , kx) = (x – 1)/2 , %3D %3D | 1-(8 + x) Find a formula for ( monok).

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Q: 3 Find The solution of X-2x+2=0 Using reton raphsen-

A: This question can be solved using the concept of Newton Raphson method of approximation of roots.

Q: 5. The function y₁=+1 is a solution of (1-2-2³)+2(1+)/-2yy=0. Find the general solution.

A: PLEASE NOTE: There is a slight  typing mistake in this question ,the differential equation should be…

Q: 6. If z = x + iy = (x, y), then the equation z²+z+ 1 = 0 is written as (x,y)(x, y) + (x, y) + (1,0)…

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

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

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Q: If C = 3x + 6 x [³y + 4z 2+²]·D= [32¹] and C = ,D -y z+

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Q: If y = f(x) is the solution of æy' + 13y – axy? = 0, f(1) = 12/a, where a + 0 is a re а, number,…

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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: