The functions f(a)= 7e and f(2)= 22" form a fundamental set of solutions of the DE on the interval (-∞0,0). Select one O True Ofalse z'y"-3ry+3y = 0,

Q: A) L{t//4} : (5/4)! a+5 B) L{u-2(t)} C) L{e"u(t)} 8- 5 3! D) L{t*e"} = E) e{icm (;)} 5Cos s(s – 2)…

A: A is false  B is false  C is true  D is false  E is false  The detailed solution is as follows…

Q: Q.2) The basts of the equatioon y'' + y" = 0,are: b) 1,1.e a) 1,1.e c) 1, x,e²* d) 1,x.e" 0 about

A:

Q: f(x + h) – f(x) f'(x) = lim h-0 %3D h bsnd Diffeentinble A) 7xh2 B) 9x2h C) 5x2 D) 9x2 5) Given (x")…

A: Given that: 4. f(x+h)-f(x)=9x2h+7xh2+5h35. (xα)'=αxα-1

Q: Solve the ODE of variable coefficients first changing this to constant coefficients x²y" – 4xy' + 6y…

A:

Q: with y(0) -1

A:

Q: Q5. Use the method of undetermined coefficients to solve (a) y" + 2y + y = x²e-". (b) у" — 2у + 5у 3…

A:

Q: The auxiliary equation of  of  y'''-4y''-4y'+16y=0  is r^(3)-4r^(2)-4r+16=0  . The auxiliary…

A: Given that fr=r3-4r2-4r+16, r∈3,6

Q: On which interval is the IVP (x sin x)y' + 2y = x +1, y(-5) = 2 guaranteed to have a unique…

A:

Q: (a) Show that y6 +x-1=0 is an implicit solution to dy dx 1 6y5 ... on the interval (-∞,1). 3 3 (b)…

A:

Q: Suppose that ye cos Bx is a solution of y-y +ay -9y =0 where a and B are real constants Then the…

A:

Q: 23 at the poles (1+i)//2 and (-1+i)//2. Find the residues of 24 +1

A: Let f(z)=z3z4+1 and it has simple poles at 1+i2  and -1+i2. The residue of any f(z) at simple pole…

Q: 9. (a) 2 Find the maximum value of 3 cos²x-8 (b) -3 (c) -5 (d) -8

A:

Q: 4) у" — 4у' + 3у %3D 4x+3е2х

A: Given:

Q: a) 12 Q.7) To write the power series £=3 4m as the form -4m a) m - 1 we must shift m to become : d)…

A:

Q: Find: (D³ - 5D² + 17D-13)y=0; y(0) = -1, y'(0) = -4; y" (0) = 17 1) 2) Roots of Auxiliary Equation…

A:

Q: (b) y" – 2y' + 5y = eª cos 2x, y(0) = 2, y' (0) = –1.

A:

Q: z.e +4 a'z cos(2x+y) z.e Solve ax 4 əx-əy axəy

A:

Q: а.) Solve x' = -5] x+ -2 [sec t] x(0) 1 b.) Solve x' = x + x(0) 1 -2 U5

A:

Q: Q.12) The solution of y" + y' = 0 by using power series method , is! %3! a) y(x) = a, – a,(1-+ b)…

A:

Q: Solve using the false rule method f(x) = /x² + 1 – tan x %3D starting at the interval [0.5,1]

A:

Q: Q.1) The general solution of the equation e' cos , is:

A:

Q: Solve

A:

Q: sec'o, Q2: Ealate vtan 9-1

A:

Q: √x³+9y³ 5x +COS (+)

A:

Q: Connider the Legendre's litterential equation Cl-x²) Y" - 2xy Any soluhion tuis" equation is…

A: Solve Legendre differential equation by series solution.

Q: f(x) = sec x As x = π-/2, f(x) =  As x = π+/2, f(x) =

A:

Q: c) y(x) = c, + cz + Acos3x + Bsin3x Q.6) The singular point (s) of (x² + 4)y" – x y' + 4y = 0 , is…

A:

Q: The function y1=ln x is a solution of xy''+y'=0 A) Find a second solution y2 on the interval…

A:

Q: (1) y "'+ y "– 2y = 3+2cosx

A:

Q: y'" If x² + y² = R² (R>0), then K Find K in terms of R. %3D V(1 + (y )² )³

A:

Q: Find the solution of the equation a²z a²z + Әх? ' дуг which tends to zero as x→∞ and has the value…

A: Given: The equation is ∂2z∂x2+∂2z∂y2=e-xcosy. Also, the given equation tends to 0 as x→0 and its…

Q: 3- Give the solution of Poissois equation マu- fcx,g) ミn e = h(x, y) in terms of corres ponding…

A: Given Poisson's equation : ∇2u=fx,y               in Ω∂u∂n=hx,y              on ∂Ω=Γ Apply Green's…

Q: 3/(a) Let X × b(n, –) and E(x)= E(16–7x) find n.

A: Solution : Given : X ~ b( n, 14 )             E(x) = E( 16-7x ) To find n : It is known that for…