QUESTION 4 For the equation (x + 1)y" - 2xy'-4y 0 a fundamental pair is: o le?x, ue*) with V= du a solution of the equation 0 = 2(x+2)v +(x + 1). dx o le ",xe2"). O None of the other alternatives is correct. (e*,In(x+ 1)e"). du ue*)with xPxz x +1 O le? dx

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

A:

Q: Ou :? u =x +y +:, x=e" cos 21, y =e"21, : =e" = e" (cos 21-sin 4t +&t +8) +2e Ob. e (cos 21 - 2 sin…

A:

Q: The general solution of y" + y = e + 5e2* is y = ei (A cos (*) + B sin )) + Ce-" + 응e2x 2 () V5z y =…

A: Given that  y"'+y=e^(-x)+5e^(2x) To find the general solution

Q: x*y"+xy'+(x? y=x cos x 2. Show that is a solution of the equation

A:

Q: y" + 4y = 2 sin 3x + 3 cos 2x Find the solution y(x)

A: Given differential equation We have to find the solution of the differential equation.

Q: y" +2y = 2x+5-e-2r y""-6y"=3-cosa

A: These questions are about ordinary differential equation.

Q: Find one solution of y" + 2y' - 2y = 3e³* cos(2x).

A:

Q: Integrate | 2 sin O de а. 3(cose)d

A: ∫2sinθ3(cosθ)2dθ

Q: 6) Find X 11 df dx by using chain rule if f=u+= cos² u G(x)= U=πX 7) Say whether the function is…

A:

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

A:

Q: еху (ay cosica) since) -y + ay²e²) dx = ) dx = (x - 5.n²cx) - 4xye Ja

A: Exact differential equation Mdx+Ndy=0 [ where My=Nx ] has the solution. ∫M (taking y as a…

Q: Find the general solution of (4) **" + 16y " – 8y'– 17y =0 y * + 8 y given that r1 = -4 + li is a…

A:

Q: a) Use the Euler formula, e¹⁰ (cos(0) + i sin(0))" = cos(n) + i sin(n). b) Suppose y(t) = e-2t eit…

A: In this question, we will find the solution to the given problem.

Q: y' + E) y = xy? 2

A:

Q: The general solution of (D²+2D +1)(D²+4)y=0 is A y=(C,+Cx)e+C,cos2r + C ,sin2r B…

A:

Q: e an is a solution or dirrerential equation y'ray=20* how?

A:

Q: \(d\) is a metric on \(X\). Show that \(\rho : X^2 \to [0,\infty)\) defined by \[ \rho(x,y) =…

A:

Q: on of y" – 2y' + 2y =

A:

Q: Q.No.3: a) Solve Cauchy-Euler equation d'y 3x3 dx3 d²y dx2 dy + 9x? + 6х— — бу %3 1+x3 dx

A:

Q: Show that (1 – e") = 2 sin ( - a eil(a-r)/2]

A: To show 1-ejα=2 sinα2ejα-π2 , simplify left hand side expression and show equivalent to right hand…

Q: Q.No.3: a) Solve Cauchy-Euler equation d'y 3x3 dx3 d'y + 9x2 + 6x dx2 dy 6y = 1+ x3 dx -

A:

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: Write a in the form a = a-T+ anN at the given value of t without finding T and N. r(t) = (3e' cos t)…

A:

Q: Given z(x, y) =In(2xy) where x(u,v)= e" cos(4v) and y(u,v)=e" sin(4v). Find ди 1 cos (4r)+-sin(4v)…

A:

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

A:

Q: Solve

A:

Q: S -1 sin y³ +1 2 dydx

A:

Q: 1) S“(cosx)" dx. 2) Г(-4). 3) В (10,9) 4) Sº x° e-2* dx Ja-x)i 5) o

A:

Q: dy z = 3e*S, y = 3z2 + sin(z) S i5I dx %3D

A: Given,           z=3ex and y=3z2+sinz

Q: 1. v₁ = (4, −2, 6, −4), V₂ = (6, −3, 9, −6)

A:

Q: tan 0 Q1:Find d do [(2 sec² y + 32 ) dy

A: Question 1 is solved. Solving more questions are against the policy of bartalby. Post remining…

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.