, Find two linearly independent solutions of 2a²y" – xy' + (2x +1)y = 0, x > 0 of the form Y1 = r" (1+a,x+azx² + azx³ + • ..) 2 = r"(1+ b,x + bzx² + bz¤³ + • . .) where ri > r2.

Q: Solve for x, y and z x + 2y - z = 0 2x + 3y - 2z = 3 -x - 4y + 3z = - 2

A: x+2y-z=0            i2x+3y-2y=3        ii-x-4y+3z=-2    iiii+iii-2y+2z=-2⇒-y+z=-1…

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: y" + 6y' + 8y = 3e-2 + 2x

A: To solve the differential equation

Q: ди a²u du +u əx² ™“əx = 0, a) at

A: We will answer the first question as we answer only one question at a time. Please resubmit the…

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: Solve using MUC. y" +4y=3sin2x 3+3+5+ y = C₁ cos2x+ C₂sin2x - -Xcos2x 4 y=C₁ cos2x + C₂sin2x +…

A:

Q: 2) x + xy+y -7= 0, (1,2) Ans. -4/5

A: We have, X^2 + xy + y^2 - 7 = 0 Differentiate with respect to x, we get 2x + [ x • dy/dx + y • dx/dx…

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: Solve for u. u/2 + 3u/4 = u/8

A:

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: What are the solutions of the equation 2sin(4x)=1 on the interval [0,n)?

A:

Q: Find a particular solution to y" + 6y + 8y = -13te³t.

A:

Q: The indicial equation of (-1) y"+ (-1)y'+2u 0 at r=1 is: (A) + 2r +1=0 (B) r1 2r = 0 (C) r-r= 0 (D)…

A: Given differential equation is (x-1)2y"+(x3-1)y'+2y = 0

Q: Solve for x: xy2 + yz2 - 4 = 2x - 1. 3-yz2 b) х %3D у2-2 a) x = *y^tyz2-3 2 с) х %3D 3 — yz2 -у? +2…

A: Consider the given expression.

Q: DETERMINE SOLUTION OF 1 x dy dx + y = x² + x (2x+3y-13) dx + 3x - 2y) dy = 0 DE

A:

Q: Solve: y" + 4y" + 29y' = 0 O y = C1 + C2e5ª cos2x + C3e5" sin2x -2а O y = C1 + C2e¬2ª cos5x + C3e¬2®…

A: The given equation is y'''+4y''+29y'=0 First write the auxiliary equation and then solve it to…

Q: Solve ,  y" - 5y' + 6y = 0

A: We have to solve  y" - 5y' + 6y = 0 (D2 - 5D + 6)y = 0 The auxiliary equation is  m2 - 5m + 6 = 0

Q: 3.a) Eliminate the Arbitrary Constants in the equation: y = C1sin(2x + C2) y" + 4y = 0 у' — 4у%3D0 O…

A:

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

A:

Q: Find the general solution for y"" + 2y" + 2y' = 0

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 an explicit solution of the given initial-value problem. 1 y(6) = 6 y = dy dx = y² x² - 1 -

A:

Q: 2) у" + 4у %3D 8x?

A: Given:

Q: 3. Find how many roots the equation 2z4 – 323 + 3z² – z + 1 = 0 - - has in the right half-plane Rez…

A: Given: 2z4-3z3+3z2-z+1=0

Q: Find a general solution of y"=(-2+2isqrt(3))y

A: Given that, the differential equation is- y''=-2+2i3y On simplifying, y''--2+2i3y=0

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: Solve: y" + 9y = 9csc3x O y = C1 cos3x + C2 sin3x – 3xcos3x + sin3xln(sin3x)

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.