Which of the following is the homogeneous solution to y" + 6y' + 25y =1 ? –3x (C, cos(4x) + C, sin(4x)) =C,e-* cos(4x) + C, e-4%sin( 3x) =C,e- cos(3x) + C, e-3%sin(4x) =e-4x ( C, cos(3x) + C, sin(3x) )

Q: y"' + 3y" + 4y' + 2y = 0, y(0) = 1, y'(0) = 1, y"(0) = 2

A:

Q: Find the particular solution : y" + y' + 16y = sin4x 1 (а) Ур — — 4sin4x (b) Ур 3sin4x --cos4x 1 (c)…

A: Correct option: C The detailed answer is listed below, kindly do like it if you find my answer is…

Q: Sara draws the 4 of hearts from a standard deck of 52 cards. Without replacing the first card, she…

A: Given, Sara draws the 4 of hearts from a standard deck of 52 cards without replacing. a) we know…

Q: What is the general solution of the given equation, cos(x + y) + 2x + (cos(x + y) + 4y)y' = 0 OA…

A:

Q: If y = cos x + sin 2x, find the value of y" - y + 3) O 2 cos x + sin x – 2 cos 2x – sin 2x O 2 cos x…

A: Given that: y=cosx+sin2x

Q: Show that D^2 = {(x, y) ∈ E^2: x^2+y^2 ≤ 1} ⊂ E^2 and the space containing a single point are…

A: In algebraic topology, two topological spaces are said to be homotopy equivalent if there exists a…

Q: integrating x and xy' - x 12 = ?

A:

Q: y' = 2aye (5)² 2 y²+y²e(#)¨+2»²e÷) 2 +2x?e(7)

A:

Q: Which of the following is a solution to x'=A(t) x + b (t) if a) v (t) = b) O v (t) = v (t) = d) ○ v…

A:

Q: Find the particular solution : y" + y' + 16y = cos4x (a) yp = -4sin4x Yp =sin4x (b) %3D %3D (c) yp =…

A: The correct option is b i.e. yp=14sin4x i.e. 14sin4x is the particular solution of the differential…

Q: The general solution of y''+4y'= 0 is ° y = C, + C,x+ C,e* ° y = C,e* + C,e²* + C;e2* -4x y = C,e* +…

A:

Q: O y = C1e- Solve 2 y" +2 y' + 3 y = 0 O y = C1e¯i" cos(x) + C2 e ¯ sin(æ) COS C;e * cos(=) + C2 e…

A: Firstly find the roots of auxiliary equation then find the general solution of the differential…

Q: y" + 4y" +y' – 6y = 2e¬t + 5 cos t y" + 4y' = 16 sin 2t , y(0) = 2, y'(0) = -2, y"(0) = 4

A:

Q: y" + 6y' + 8y = e-³te5t, y(0) = 0, y'(0) = 0 a. (e³t-1)²e-5t 3 b. (et - 1)³e5t a C. (et - 1)³e-5t 3…

A: The given initial value problem,.We have to find the solution to the IVP.

Q: The general solution of y" + 4y' = 8, can be written as (A) y = c1 + c2e¯2« + c3e²a + 3x (B) y= c1 +…

A:

Q: Find the general solution of the nonhomogeneous equation y4) + 2 y "+y=cos( 3 x) + 2 1 a) y =C,…

A: We will find out the required solution.

Q: -5 -4 -3 -2 -1 n y = دیار 2- 7 1 -2- -3- -4 2 3 4 10 5 Write an equation for the function graphed…

A: Given graph

Q: Find the singular solution to the Clairaut equation y = xy' + In(-27 - y'). none y= 13 x +1 –…

A: General solution to the clairaut equationy=xy'+ln(-27-y')is given by y=cx+ln(c)Now, differentiate…

Q: (z³+2)“ (4z+3z²)³ What is the first derivative of y = (z³+2)°(51zª+20z'+48z+32) O y' = (4z+3z?) %3D…

A:

Q: y""+y" = 3x² + sin x - 2 cos x

A:

Q: Let y, be a solution to y" + zy +r'y = cos (z) and y, be a solution to y" + zy' + z*y = sin°(z).…

A: Given that y1 be a solution of y''+xy'+x2y=cos2x and y2 be a solution of y''+xy'+x2y=sin2x. That is,…

Q: When the general solution of y" + 4y = tan2x is written as y = U(x)cos2x + V(x)sin2x then which of…

A: The given differential equation is y''+4y=tan2x. The auxiliary equation of the corresponding…

Q: y" +2y+3y= sint + 8(t-3л); y(0) = 0, y'(0) = 0

A:

Q: -7x f(x, y) = e" sin(4x + 5y) af e^(-7x)(4cos(4x+5y))-7sin(4x+5y) af 5e^(-7x)cos(4x+5y) dy ||

A: Partially differentiate with respect to x and y by using product rule.

Q: xt' + (t")3 = Và +5 x (3y')² ex² - y² = = (4x²y³ + y)²¹ y" 4 (cos x)² - y"

A: The given  differenrtial equation is xt'+t''3=x+54 Calculate the order of given differential…

Q: The general solution of 4y"+4y' +y = 0 is ()%3D

A:

Q: y" — 5y" — 14y' = (2x - 1)e-29+ s

A: y"-5y"-14y'=(2x-1)e-2x-9+sin7x -4y"-14y'=(2x-1)e -2x -9+sin7x

Q: y sin 2x + cos 2y = ax Find y' a – y cos 2x y% = sin 2x – sin 2y а - 2у сos 2x y sin 2x – 2 sin 2y…

A:

Q: Find the particular solution : y" + y' + 4y = cos3x 3 5 3 5 (a) cos3x -; sin3x (b) Yp = cos3x -…

A: Proceed as shown below...

Q: Solve the initial value problem y y" +2y-8y = 9 Cosx-2 sinx yea) = 4, y co) = -6

A:

Q: y" - 5y'=x-2, when x = 0, y = 0, y = 2

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.