The general solution for Legendre equation (9 - z)y" – 2zy' + n(n + 1)y = 0 is O y(z) = c,Y1(1/3) + c2y2(x/3) O y(1) = c¡Y1(z²/3) + c2Yz(z²/3) O y(x) = c¡Y1(3z) + c2Y2(3r) O y(x) – c1y1(3x²) + c2¥2(3x²) O none

Q: Consider the equation y"-y-2y = 0. Assume that y₁ (1) = ¹ and y₂(1) = e² form a fundamental set of…

A:

Q: The general solution of (D³+4D)y=0 is (A) Ay=c₁еx+c₂e²x + c3e² (в y=e*(c₁cos2x+c₂sin2x) -4x y =…

A:

Q: d a value of r> 0 such that h(z) = z² +22³ + z + 1 has all its zeroes in D,(0).

A:

Q: Let y1, Y2 be two independent solutions of (t – 1)y" – ty' +y = 0. If W(y1, Y2)(2) = e² , then W…

A:

Q: (b) -x X x + y y - 4y + 2z = - - (x, y, z) = 10 Z = 2 z = 1

A:

Q: Let y1, Y2 be two independent solutions of (t – 1)y" – ty' + y = 0. If W (y1, Y2)(2) = e² , then…

A:

Q: Find the solution of 4x²y" – 6x²y' + y = 0, x > 0 %3D of the form Y1 = r"(1+ c,x + czx² + czx³ + • ·…

A:

Q: (D³ - 3D - 2)y =0; when x =0, y=0, y' = 9, y" = 0. A y = (-1+ 2x)e²"+2e=x B y = (-1+ 2x)e-2r+e2r C y…

A: Given differential equation is (D3-3D-2)y = 0 with x=0,y=0,y'=9,y''=0.

Q: 2) z(x, y) = (x² + 5y)³ (3y + 2x)

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

Q: Solve y'-y y'e" A) y(c- x) = e", y= 0 B) y(c – x) = 0, y = 0 C) y= e", y = 0 D) y(c-x') = e", y= 0

A:

Q: Find the solution of (2*y² – y) dx + (x²y* – x) dy = 0 o를 +를 - C O 3r°y + 2ry* – Czy = 6 %3D o +를 +금…

A: Please see the answer below

Q: (C) y" + 21y+8x=y" + 5y' + e²*

A:

Q: Let y1, Y2 be two independent solutions of (t 1)y"- ty' +y = 0. If W(y1, Y2)(2) = e2, then W(y1,…

A:

Q: Solve the equation (x + 2y-4)dx - (2x + y - 5)dy = 0. (x + y - 1)² = c(x-y-3) (x-y-1)² = c(x + y -…

A: x+2y-4dx-2x+y-5dy=0

Q: 2x- (ii) Given aty=b²x-y and a 4x+3 = bx-5y, show that 3y-6x=7x² +5y²

A: (ii) Given ax+y=b2x-y and a4x+3=bx-5y We will use logarithm properties to solve the given:

Q: (D) e(-1-v2)x + cze(-1+v2)x If r2+2r-1 = 0 is the characteristic equation of a homogeneous D.E. with…

A:

Q: 7. Given 2x2y" + xy' + 3y = 0 show that 2x2y+2) + (4n + 1)xy"+1) + (2n² – n+ 3)ym) = 0 %3D

A: We use the method of mathematical induction to show the given statement holds (given…

Q: 30. Which of the following is the value of f.(2, -1)? O -13 O 50 O 106

A: Given :              f(x, y) = 2x3 + 7x2y3 + 8y3 + 3x - 2y + 10   To find the value of fx(2,…

Q: Find the general solution of dy/dx = (x - 4) / (6 - 5x + x^2). O y = 2 In(x - 2) - In (x - 3) + C y…

A:

Q: (c)2a) (c)(n)(z)(z) = e/(a) (c)(K)(z)) ¹/2 (b)(y) (6)(x) (y) Solve for K [(g) (m) (f)(K)

A: We have to solve for k.

Q: Find the general solution of (1) yV – 2y" + y" = 24x² + 12x +8

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: b) y(4) + y(3) – 7y(2) – y' + 6y = 0. c) y(4) – y(3) – 7y(2) + y' + 6y = 0.

A: Solve the given differential equation Here I am giving answer of 1 st problem if you want answer of…

Q: Consider the equation y" + ay' + by = f(x) the constants a and b are real and different from zero,…

A:

Q: What is the particular solution if y(1)=0? 1/2 xy = y + (x² + y³)"

A:

Q: y=cJ,(/2x) +c,J,(/2x)is solution for x?y "+xy'+ (2x² – 4) y=0

A: Given, y=C1J42x+C2J42x is solution for x2y''+xy'+2x2-4=0 To find that this statement is true of…

Q: 5. Find the general solution of (D³-D)y=4e*+3ex. Ans. y=2xe*+(1/2)e2+c1+c2e*+c3e*

A:

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.