2. b. Find all solutions of the equation P(x) = 0. Write complex 02 メ8+zX %3D 1

Q: ;y(0) = 1 form of yp to solve

A: As per the bartleby guidelines for more than one part only one has to be solved .Please upload the…

Q: If y, and y, are solutions of a non-homogenous equation y" + ay' + by = c , then y, - y2 is a…

A: Since y1 and y2 are two solutions of the non-homogeneous equation, we have y1''+ay1'+by1=c…

Q: . Find the general solution of the first-order equation y? – 2ry dy dr

A:

Q: the solution of the homogenous equation (хусот х -)dy - Ydx = o

A:

Q: 12. (D² + D)y = -cosx %3D

A:

Q: Find the general solution of the D.E (D^2+4)y=sin3x

A: We have to solve the problem

Q: Obtain the general solution: 1. (D² + 25)y = -50 sin 5x

A: First we will find the complementary solution corresponding to the homogeneous part of the…

Q: Solve the following equations y" - 4y + 4y = 8x² + 4x y" - 2y - 3y = sin 2x

A:

Q: 5. Given that a cubic equation x" + ax" + bx +c = 0 has zerOS a, B and y. Show that aßy = -c.

A:

Q: Solve the first order equation (3r²y + 2ry)dz + (z³ + x² + 2y)dy = 0.

A: In the given question, the concept of the differential equation is applied. Differential Equation A…

Q: Solve for z. If there are no solutions type DNE: 1 -4%3= I- 4 4z - 16

A: x4x-16-4=1x-4

Q: Find a second solution to 4x²y" +y = 0, given one solution y1(x) = x!/² In x.

A: Given differential equation 4x2y''+y=0.....1 And given one solution is y1x=x12lnx Equation (1) can…

Q: eУ + 2ху'- у %3D0

A: Given equation is, ey'+2xy'-y=0y=ey'+2xy'...1 Multiplying by y in equation (1), we get…

Q: 1-y2 11(x² + y²)10 dxdy .

A:

Q: (1-x)y" - 2xy + n(n+i)y =0 [ Legendre Equation] |

A: We will solve it by power series method

Q: 3) Solve y"-4y't13y y0)=-l sy'co)= 2

A: The given differential equation is                                                     y''-4y'+13y=0…

Q: Find the general solution of the equation y" - 4y' + 13y = 12e2 sin 3x.

A:

Q: y" – 2y' + y = –3 – x + x²,

A:

Q: (D++D²)y=3x²+4sin(x) – 2cos(x) 2. MUC:

A: The given D. E. is  (D4+D2)y=3x2+4sin(x)-2cos(x)

Q: Determine the appropriate form for a particular solution of the fifth-order equation(D - 2)3 (D2 +…

A: Given differential equation is D−23D2+92y=x2e2x+xsin3x......1. We have to determine the appropriate…

Q: 5. Given that a cubic equation x° + ax² + bx +c= 0 has zeros a, ß and y. Show that aßy = -c.

A:

Q: Solve the Bernoulli equation. 3xy' + y = y¯8 x>

A: We have to solve

Q: Show that the general cubic equation y3 + by2 + cy + d = 0can be transformed into an equation of the…

A: To find the equation of the form

Q: 2 Y Sin y - yy 3=c C- %3D

A:

Q: Q5. Use the method of undetermined coefficients to solve (a) y" +2y' + y = x²e¬ª. (b) у" — 2у/ + 5у…

A: We are entitled to solve only one question at a time. As the specified one is not mentioned, So we…

Q: 6. Find all solutions to the Diophantine equation 17x + 19y

A:

Q: 2. Solve the diophantine equation x = y'.

A:

Q: Solve the general solution y4 + 2y" + y = x² sin x

A:

Q: The equation y3 = 3Bx is the general solution of 3y Oy Oy 3xy Ou' = 3y

A: We will form the differential equation using given solution

Q: If y and y, are solutions of a non-homogenous equation y" + ay + by =c then y,-Y2 is a solution of…

A:

Q: y" + 2y' = 2te

A:

Q: Transfer the Cauchy-Euler equation to a constant coefficient equation and find the general solution;…

A: We have to transfer the following Cauchy-Euler equation to a constant coefficient equation and hence…

Q: solve the given equation below: xy'=4y

A:

Q: 4. Solve the equation z3 + 8i = 0

A:

Q: Q2-5 * Solve the he (D-3D+2)y(x)= sin(e™") equation

A:

Q: Find the general solution to the equation 4(x^2)y''+8xy'+y=0 by the method of Frobenius.

A: The differential equation is 4(x2)y''+8xy'+y=0. Let the solution be y=∑n=0∞anxn+r, then its…

Q: Obtain the general solution: 1. (D² +25)y = -50 sin 5x

A: Using method of linear differential equations with constant coefficient.

Q: Make a real life problem and solve it using the george polya's step in solving it

A: George polya's steps is an algorithm which consist four parts to solve a problem 1)Understand the…

Q: Non Homogeneous LDE solve: (D2  +  D  -  2)y  =  2x  -  40 cos 2x

A:

Q: Using the detemmmant Solve for 2 -2 zy 24 पु पूुड =42

A:

Q: Find the general solution of each nonhomogeneous equation. 1. y" + 4y= 8

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: (b) Solve y -4y = (r – 3) sin 2x, by the method of undetermined coefficients.

A:

Q: AC 8x-14 and EC = 2x+11. solve for z. %3D %3D B. D.

A: If AC=8x-14 and EC=2x+11, solve for x

Q: 10. Solve the equation for the exact solution. TC arccos y- 3 %3D 6.

A: Given, arccos(y-π/3)= π/6 Multiplying both sides by cos we have, (y-π/3)= cos(π/6)

Q: 2. Solve the exact DE and give the general solution. a. (4y-3x)y'-3y 0

A:

Q: 1) Consider the equation y'+2x y-y'=-2x, x>0. (a) Determine the values of the constants k and r such…

A: On integrating, Note:- order of differential equation is number of constant. In Part(a) solution…

Q: Solve the bernoulli's equation x(6x^2−y−1)dy +2ydx =0.

A: The given Bernoulli’s equation can be written as:

Q: 3/2 X2 dx

A: 1.∫x32tan-1(x) dxlet x=tdiff o.b.s12xdx=dt dx=2t dt∫t3tan-1(t) 2t dt=2∫tan-1(t) t4 dtwe know that…

Q: 2. Determine the general solution to the equation y' + 2xy = e-2". %3D

A:

Q: Find the general solution of y"+25y=sec(5x)

A: