3) i A) { B) [- Consider the homogeneous DE: y'"" + 2y" + y = 0 Verify that y = cos(x) is a solution of the DE. ! Find the general solution of the given DE.

Q: Determine a suitable form for Y (t) if the method of undetermined coefficients is to be used. y" +…

A:

Q: Express the equation r = 3 cos 0- 12 sin 0 in Cartesian coordinates. (x² + y²) – 3r + 12y = 0 + y²)…

A:

Q: Find the solution of x²y" +5xy' +(4+4x)y=0, x > 0 of the form n =1,2,3,... where co 1. Enter r = =…

A:

Q: Consider the equation 4y" + by' + cy = 0 the constants b,c,m,n are real and different from zero, the…

A:

Q: Q1) Solve the BVP ut = Uxx+sin 2x, 00 u(0,t) = 0, u(π, t) = 0 u(x,0) = 0

A:

Q: 8. Use change of variables to find: a) The Jacobian if x=(u+3v), y =; -(v- 2u).

A: We will use concept of change of variables.

Q: a) Find the relationship between Ju(x) cnd je(x) by comparing the invariont forms of [x;, x, x- r?]…

A:

Q: a) Use the d'Alembert solution to solve UTM UTM &UTM -00 <I < 00, t20, UTM 1Pu 9 dr u(r,0) = cos r,…

A:

Q: 1.( ) L(t sinh t) = -A) 2.( ) Let z1,, be complex, then Arg(z, +=,) = Ar 3.( ) Let "-y'+ 2r = In (t…

A: Note- Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: 7. Find the rectangular equation if r = 4 cos 0 + 4 sin 0 (a) (c) x² + y² = 4 x² + y² = 4(x + y) (b)…

A:

Q: where co= 1. Enter T= s) Find the solution of z²y" + 5ay + (4-4x)y=0, z> 0 of the form Cn= , n = 1,…

A: Given a differential equation and y1 is it's solution. ..then we doing derivative  of y1 and putting…

Q: sinr where 0sI<R 3. a) Evaluate LF())where F()-o where t2 dy de 3x-3y+4 and dt = 2x-2y-1 dt b) Solve…

A: see below the calculation and explanation

Q: If e* and xex are solutions of y"tay'tby=- Are soluhons linearly independent? write the soluhion.…

A: Given that e−x and xe−x are the solutions of y''+ay'+by=0. We have to check whether the e−x and xe−x…

Q: Which of the following is a solution of y" + 2y' – 15y = 0 а) sinx b) еЗx c) x? d) e5x

A:

Q: a) Use the d'Alembert solution to solve UTM Pu 1Pu AUTM UTM -00 0, UTM 9 ar u(r,0) = UT = cos r,…

A:

Q: (7) Show that the given functionis an integrationy factory Solves a) Sinydx+ Cosydy =0(e),…

A:

Q: : Mark all the ODEs in the list for which the function y(t) = cos(t) is a solution. A) y' = sin(t)…

A:

Q: Show that u(x, y) = e³ cos x is harmonic and find the harmonic conjugate v such that v (0,0) = 0.

A:

Q: Find the general solution to the hypergeometric ODE #(1 – 2)y" + (; - 2-) a - - 0. 3 ) y y = 0.

A:

Q: 4. Solve the Euler equations: a) x²y"-xy'+y = 0

A:

Q: 4. Verify that the functions 1, r, cos r and sinr form a funda- mental set of solutions of y(4) + y"…

A:

Q: 1.Find a general solution of each O.D.Es. A) y" 19y = coqx +os 3 - šin 2 (3) y" + 4y/ + 6.25у —…

A: First we determine the general solution of the related homogeneous equation.  auxiliary…

Q: (a) Show that a differentiable function f decreases most rapidly at x in the direction opposite the…

A: Fastest decrease occures opposite to gradient .Explanation:Step 1: Step 2: Step 3: Step 4: