1. Show that the given functions are solutions of the given differential equation? (20 pn) x²y" + 5xy' + 4y = 0, y1 1 = and х2 .2 In(x) Y2 = x2

Q: 1. Find the general solution of each of the differential equation y" – 2y' +y = 0.

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 2. Show that k(x, y) = e2ª cos (x + In y) is a solution to the differential equation 2k – ykya = 5k.

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Q: Show that the y,(2) = K, (1 – 2x* +*-*-)* * (2x -+ 4 x6 + ... 45 4 + K2 (2x 4 8 + ... 3 15 315 is…

A: we have given yh(x)=k11-2x2+23x4-445x6+...+k22x-43x3+415x5-...is complementary solution of…

Q: A. Obtain the differential equation of the given solution by eliminating the arbitrary constant(s):…

A:

Q: 4) In the differential equation of, y(x³ – y)dx – x(x³ + y)dy = 0 where a and ß are constants, what…

A: Question from ordinary differential equations.

Q: 1. Find the general solution of the differential equation (1+ 9x²) cos y dy – 3(1+ sin y) dr = 0.

A: we have to solve this by separation of variable

Q: 6. If the function y = a, (1 + 3x + x² + r- :) is a solution of the differential +. equation Ay' –…

A: The solution is given as

Q: 4. Find the general solution of the differential equation using the method of undetermined…

A:

Q: 1. Find the general solution of the given differential equation using MUC: y(4) – 4y(3) – 21y(2) +…

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Q: 1-Apply the undetermined coefficients method to find a particular solution of the following…

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Q: 4. Find the general solution of the differential equation using the method of undetermined…

A: Let's find.

Q: 1) Use the Method of Undetermined Coefficients to find the General Solution to the Differential…

A: Given : Differential  equation is            y'' - 4y' - 12y = 2sin(t) To find: Find the general…

Q: Find the particular solution of the following linear 1st order differential equation which satisfies…

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Q: Find the general solution of the first-order linear differential equation for x > 0. (Use C for any…

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Q: 6. Find the particular solution to the differential equation: (y +2)y"=3x*y+4y, given: y(0) = 1…

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Q: 1) Solve the Bernoulli differential equation with the given initial condition. x-2xv = 3y“, >0 =

A: Given: x2dydx-2xy=3y4  The initial condition is:  y1=12 Dividing the give equation by x2 , we have:…

Q: (b) Consider the differential equation ydx + x(lnx-lny - 1)dy = 0. Hence, or otherwise, use an…

A: Let us consider a differential equation of the form Mdx+Ndy=0 To equation is exact if ∂M∂y=∂N∂x then…

Q: Determine the values of r for which the differential equation 2y"+ 5y'- 3y = 0 has solutions of the…

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Q: 4 (a) Identify the homogeneity of the following second order differential equation and state the…

A: Given second order differential equation  3d2ydx2+5y=2y''+1 A second order differential equation…

Q: 16. What is the particular solution of the linear differential equation y' +y = sec e", whose…

A: The solution is given as

Q: 3. The Bernoulli's form of the differential equation x' ydx+(3x - y³ dy=0 is

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Q: 2. Solve the nonhomogeneous differential equation, using the basic rule: y(2) + 6y(1) + 9y =…

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Q: The particular solution of the following nonhomogeneous differential equation y" - 2y' +y = x? + e*…

A: To find  The particular solutions of the given differential equations

Q: x2+1 y'= Ans: y = + x + In(x – 1)² +c = -X - X-1

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Q: 1. Find the general solution of the given differential equation using MUC: + 104y(1) – 80y = x² e2x…

A: We can solve this using given information. y4-4y3-21y2+104y1-30y=x2e3x+3-5cos3x First we find the…

Q: 6. Use the method of variation of parameters to find a general solution to the differential equation…

A: First we find the complementary function yc and particular solution yp The general solution is then…

Q: 5.- Use the method of undetermined coefficients to find a particular solution, Y, , for the given…

A: Take up in perfect form and put on the given differential equation

Q: 1. Find a homogeneous linear differential equation with constant coefficients whose general solution…

A: Given:y=C1+C2x+C3e-7x

Q: 4. Show that the coefficients of the given differential equation are homogeneous and solve the given…

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Q: Consider the differential equation y 4xy (In y)² Find the solution that passes through the point (0,…

A: Given  y'=4xy(lny)2. The main objective is to solve the given differential equation with the initial…

Q: Show that In y | In x dy = 0 dx +|1+ is an exact differential equation. Hence, find the solution.

A: The given differential equation is                                                         1+ln…

Q: 1. Let the following higher order differential equation (1) y" – 2 y" – 3y = 3e. Determine the…

A: Given y'''-2y''-3y' = 3e5x                               1The auxiliary equation for homogeneous…

Q: 4. Find the general solution of the differential equation using the method of undetermined…

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Q: [1] Verify that y = e3* cos 2x is a solution of the differential equation y"-6y + 13y = 0

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Q: 1) Solve the Bernoulli differential equation with the given initial condition. -2xy = 3y", 0 =.

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Q: A. Obtain the differential equation of the given solution by eliminating the arbitrary constant(s):…

A:

Q: Determine the values of r for which the differential equation y' +9y = 0 has solutions of the form y…

A: Given differential equation.

Q: 1. Use the undetermined coefficients method to find the general solution of the given differential…

A: Since this image is asked for multiple answers, as per our answering guidelines we are supposed to…

Q: Write down the form of the general solution y = y. + y, of the given differential equation in the…

A: Consider y=emx be the solution of the homogeneous part. The auxiliary equation is m2+w2=0. Simplify…

Q: 2. Find the solution of the differential equation ₂ dy 2x² = dx 3xy + y². which satisfy an initial…

A: Solved below.

Q: 5. Find the general solution of the given differential equation y" + 3y" + 3y + y = 0

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Q: 4. If y, (1) = a is a solution of dy dr Find the second linear independent solution and the general…

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Q: determine the general solution to the given differential equation on (0,∞). Q. x2y′′+3xy′+y =0

A: Differential equation: x2y''+3xy'+y=0Now we put a substitutionz=log…

Q: (b). By reversing the role of x and yY or otherwise, find the general solution to the differential…

A: Given:        2x-4y2dydx+y=0            2x-4y2dy+ydx=0    Equation in total differentials:…

Q: 12) Consider the differential equation y" + a1(x)y' + ao(x)y = 9 sin(7x) And suppose that Y1 = x Y2…

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Q: 1. Let the following higher order differential equation y" – 2 y" – 3 y = 3 e5= (1). %3D Determine…

A: Solution by using the method of variation of parameters is given as follows :

Q: 1. Find the general solution of the given differential equation using MUC: y() – 4y(3) – 21y(2) +…

A:

Q: 11) Consider the linear differential equation y" – ly = 2e6z + 3x + 8 If the particular solution has…

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.