Solve the following problems by the method of undetermined coefficier 1. (D² – 4D – 5)y = x² – 2x + 3 2. (D² – 5D – 6)y = 18x² + 12e2x 3. (D² – 5D + 6)y = 15 sin x – 15 cos x

Q: C. Solve the nonhomogeneous ODE. y" + 2y' + 5y = x² + cos3x

A: To solve the following differential equation  y" +2y' + 5y = x2 + cos3x

Q: Find the general solution: y" – 2y" + 4y' – 8y = sinh 2x

A:

Q: Which of the following CANNOT be solved by method of undetermined coefficients? A (D2-3D+2)y=sin x+…

A: Given that:

Q: 4. Show that y=e²* sin 3x satisfies the equation: y" – 4y' + 13y = 0 %3D

A: Topic = Differential equation

Q: Find the general solution of the equation d2y/dx2 - 2dy/dx +4y =2ex sin2(x/2)

A: Given the given differential equation is d2ydx2-2dydx+4y=2exsin2x2

Q: Use Method of Undetermined Coefficients: y" - 2y' + 5y = 4e*cos2x +x2 2

A: We have given a differential equation ,  y'' - 2y' + 5y = 4ex cos2x + 52x2 First we will find…

Q: Find the general solution of the equation d2y/dx2 - 2dy/dx +4y =2e sin2(x/2)

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Q: Q3) Solve (ysin x + y²) dx – („ - 2xy) dy = 0 + cosx %3D |

A: A differential equation of the form Mdx+Ndy=0 is said t be an exact differential equation if it…

Q: Show your complete solution in finding the General Solution of (D² + 4)y = sin 3x . Use method of…

A:

Q: d²y Find the solution for cos(x) (1+ x²) – 2xy = with the conditions %3D dx2 1+x2 y(1) = -1, y(2) =…

A:

Q: 2as L{t sin(at)} = %3D (s²+a²)²

A: We can derive it using the definition of Laplace transform or by using some identify or formula.

Q: 2. Find a particular solution using Undetermined Coefficients to: y" + 2y' – 3y = f(t), where f(t)…

A: As per our company guidelines, we can solve first question for you. If you want other question to be…

Q: c. T(x) = x (**-cos(2x)). find Q at x = t/4. d. T(x) 100e-3x + In(4x), k=470, A= 0.01r and x= 1/3;…

A: c) Given, T(x)=x(x2-cos(2x)) at x=π2

Q: 4. y" - 5y' + бу %3 -sin(2x)

A:

Q: The equation y C₁e(x) cos3x + C₂e(-x)sin3x is the general solution of O A.y" - 3y + 10 =0 OB.y" + 2y…

A: This y is the general solution ,when the roots of the auxiliary equations are -1+3i and -1-3i

Q: 2x Show that y = e²* sin 3x satisfies the equation y"-4y'+13y=0.

A:

Q: y''''+8y'''+32y''+64y'+39y=e^(-2x)((4-15x)cos3x-(4+15x)sin3x) Find a particular equation for:

A: The given differential equation is: y''''+8y'''+32y''+64y'+39y=e-2x ((4-15x) cos3x-(4+15x) sin3x)…

Q: Q7// find the general solution 1 (sin-ix + =y)dx + sec-1xdy = 0 xVx² – 1

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Q: Solve the following problem with the fourth-order RK method: d²y 2 + 3-+3.125y = sin x dx2 dy dx…

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Q: Determine the most appropriate method to find the general solution for the functions: y" - y' - 2y =…

A: Given differential equation is y''−y'−2y=2x+sin2x−4hcos2x. We have to determine the most appropriate…

Q: solve for the ganeral solution.  y' + x-1y = cos(x2)

A: Find the general solution.

Q: Solve the following DE using the method of undetermined coefficients: a. y"-3y'+2y= 20xe3x b.…

A: a) y''-3y'+2y=20xe-3x Auxiliary equation m2-3m+2=0 m2-2m-m+2=0 mm-2-1m-2=0 m=2,1 yn=C1ex+C2e2x and…

Q: SV1- x2 sin-1x dx

A:

Q: The general solution of (D²-2D+1)y=2sin x A) y=ce*+C2xeX+sinx B) y=c1eX+C2xex+cosx y=C1eX +C,XeX…

A:

Q: Q7// find the general solution (sin-1x + 1 y)dx + sec-1xdy = 0 1 xVx² – |

A: The detailed solution is as follows below:

Q: Which of the following CANNOT be solved by method of undetermined coefficients? 1 A (D²+1)y=- cos x…

A: Method of undetermined coefficients is only applicable for differential equations with…

Q: d²y 9. +y= sin 3x cos 2x 2

A:

Q: Find a particular solution to y" + 16y = 16 sin(4t). Yp

A: The given differential equation is:y''+16y=16sin4t        ...............(1)The auxiliary equation…

Q: b) y" + y' = sin 2x

A: here we need to find the particular solution of given differential equation. the solution is…

Q: Solve the following initial value problem using the undetermined coefficients method: d²y dy 5- x-…

A: Given equation is, Now take, then, Hence the complimentry solution is,

Q: 4. (D² – 3D+ 2) y = 14 sin 2x – 18 cos 2x -

A: From the given differential equation; D2-3D+2y=14sin2x-18cos2x So, the auxiliary equation is:…

Q: a. Solve the initival value problem: y = 5 cos (2r)/(6+ 5y), y(0) = -1. -6+V36 - ( sin (x) + 10 2. A…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Q21// find the general solution (sin²x + 2ye²x + 2)dx + (e2x – sec²y) dy = 0

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Q: 3. y"+16y = x cos 4x + e* sin 4x +3e 4x

A:

Q: f(t) = e¯3t cos ( at + cos ( 2at + 3 2

A:

Q: Find the general solution of: y"-3y 8e* + sin 2-

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Q: Find the complete solution of d2y/dx2 + 2dy/dx + y = sin x cos 2x.

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Q: 2. Solve the DE: 2y' - y= 4 sin( 3x)

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Q: Solve the following equations: a) y√(1-x²)dy + x√(1-y²)dx=0 x(2 ln x+2) dy = b) dx sin y+y cos y…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: What is the solution of D.E (D2 - 2D)y = e sinx when solved using the method of undetermined

A:

Q: Find the general solution: y" + 5y' + 6y = 4e¬t cos2t + sin2t A - BI -

A: Differential equations

Q: nd the particular solution using the method of undetermined coefficients. dx – 2x =-3+4 cos t dt

A:

Q: Find a particular equation for: y(4) + 8y''' + 32y'' + 64y' + 39y = e-2x[(4 - 15x) cos 3x - (4 +…

A: The given equation can be written as, y4+8y3+32y2+64y1+39y=e-2x4-15xcos3x-4+15xsin3x it is also can…

Q: Find the particular solutions satisfying the given conditions: dy a) y = 2 when x = 0. dx = 1 + cos…

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

Q: Use undetermined coefficients to find the particular solution to y" + 4y' – 5y = – 1360 sin(3t) %3D…

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

Q: Solve the following initial condition problem: d2y/dx2 + 9y = 2 cos(3x); y(0) = 0; y′(0) = 1 /3

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Q: Find the solution of d2y/dx2+4y=sin3x+cos2x

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Q: 2. Solve the following equations: d²y dy а) 8 + y = 2x + 40 sin x dx - dx2 d²y b) 2 dy + 2y = 2 sin…

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Q: Find the general solution y" +4y'+5y=2e +cos.x -2x

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