(Find the family of solutions of the separable equation): (x − 5)y² – ²²(y² — 4) - a) In r+-+=y=0 b) +-Inyl + = c;y=0 c)² + + + In|y| = c; y = 0 d) In r+-In y-=c;y=0 e) In r[++-=c;y=0

Q: Let p and q be the two roots of the equation mx? +x(2-m)+3=0. 2 Let m,, m, be the values of m…

A: Given mx2+x2-m+3=0        ...(i)

Q: Hind the cooffecPents + ax tb=0, where c = 3 anod x =-2 are tha roots a anod b f1om the oquatfon,

A:

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…

A:

Q: a) f(z) = vz+Vz - 1 b) f(z) = Vz2 +9 %3D

A: A branch point of an analytic function is a point in the complex plane whose complex argument can be…

Q: 9) Solve: (x + y)dy-(z-y)dx=0 a) x² + y² = C b) z² + 2xy + y² = C c) z²-2ry+y²=C d) z²-2ry-y²=C

A: We need to solve D.E.

Q: 4) Solve the Cauchy euler equation x- 3x2+ 6x2-by = 3 + Inx dr

A:

Q: , Find two linearly independent solutions of 2a²y" – xy' + (2x +1)y = 0, x > 0 of the form Y1 = r"…

A: (Note: Please scroll to the last step for the final answer.) Given equation is 2x2y''−xy'+2x+1y=0…

Q: Show that the equation 24 = (-5 – i/T) z+(60 – 80 i) has no solutions in the closed disc z| < 3.

A:

Q: 2) z(x, y) = (x² + 5y)³ (3y + 2x)

A: Let's find dz/dx and dz/dy.

Q: 6. (E) Prove that there are no solutions to the equation 2x² + 5y² = 32² in positive integers (x, y,…

A: Given equation is    2x2+5y2=3z2  ------ (1)  Let's suppose that we have a solution x,y,z where…

Q: 23 at the poles (1+i)//2 and (-1+i)//2. Find the residues of 24 +1

A: Let f(z)=z3z4+1 and it has simple poles at 1+i2  and -1+i2. The residue of any f(z) at simple pole…

Q: Q.10) 412-8/-12 Solve 1-3

A:

Q: 5. Use the method of undetermined coefficients to solve (a) y" +2y' + y = x²e¬ª.

A:

Q: b) Use xo = 1, X₁ = 1.5, x₂ = 2 to find the second interpolating polynomial to 3 f(x) = 2x+1

A:

Q: Why did we plug in x = 1/2 at the last part of the solution for the second problem

A:

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

A:

Q: y"+y' + (a) -5 x-b = 0, Xo = 2 is 5. (b)-3 (c)-2 d)-8 Q7) L(y") = a) s²L(y(x)) + sy(0) - y'(0) c)…

A: We have given the answer in the next step. Hope you understand that

Q: 7) Find the general form for solutions of y (s) + 8y (²) _qy² = 0 Answer should be y= A + Be* +Ce* +…

A:

Q: Q6 : find 1) j(1 – jv3)(v8 +j) 2) (1+j)(1– j/3)² 3) cos-1(2)

A: (1) j(1-j3)(8+j) Use the property (a+b)(c+d)=ac+ad+bc+bd in the expression (1-j3)(8+j) and…

Q: 16) Let f(m)-0 be the auxiliary equation of f(D)y=0 with solution set equal to (-1,0,0,2), then…

A:

Q: 5) x2. dx = x² + 3xy + y², (c) dr = 2 = 3v, + 3x' (d) (1 - y)' + By - 5x = 0.

A:

Q: D

A:

Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

A:

Q: Q19) The general solution of 2x²y" + 3xy' - 15y = 0, is: a) y(x) = = ₁x² + ₂x³ b) y(x) = c₁x + ₂x-3…

A: As per our company guidelines, we are supposed to answer only the first question. Kindly re-post the…

Q: Look for the annihilator of the given expressions. i) e2x sin3x ii) x³ e4x iii) 5x* - 2.x + 8x - 7…

A:

Q: Select all equations that are equivalent to a-6z 16. a + 6x 9 0 O b a + 6x +9 = 16 Oc a+6x + 9 = 25…

A: Solution:-Given equation,     x2+6x=16  —1let us see and solve each option given,a…

Q: Find a particular solution to -18.5e-2t y" +4y +4y = 12 + 1

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: If y1, Y2, and y3 are any solutions of y" – 6y' + y = 0, then so is 4y1 – y2 +y3 -

A:

Q: Solve the equation: y" -y = 2* + Oy=ce to xe +e* (x+c3e2X + CA) Oy=c₁e* + c₂e* + ex (x + c3e-²x +…

A:

Q: Determine which of the following equations always valid (give an algebraic proof) are: (Q59) a'b +…

A: Boolean algebra plays a crucial role in digital logic design, providing a framework for analyzing…

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