Q3.The following equation models a spring that receives an initial shock and then an aftershock half as strong 5 units of time later. 1" + 4x' + 20x = 26(1) + 6(t – 5), r(0) = 0, x'(0) = 0. What is r(6)? e10 sin(4) + 2 sin(24) b) he2 sin(4) + 2 sin(24) e10 sin(4) + 2 sin(24) 4e12 e10 sin(4) + 2 sin(8) d) 4e12 4e12

Q: The motion of a mass on a spring is described by 3y" + 4y = 0, y(0) = 5, y'(0) = 6. What is the…

A: Given:The motion is described by 3y''+4y=0, y0=5, y'0=6. We have to find the amplitude of the…

Q: 7. What is the value of (X-2)2 for the scores 2,3,5?

A: To find : ∑X-22 for the scores 2, 3, 5

Q: Given f''(x) = – 9 sin(3x) and f'(0) = – 4 and f(0) = 5. %3D %D Find f() =

A:

Q: (6) [²/2 sin² (2) cos2 (x).dx = A) 플 B) 플 C) 미플

A: We need to make it proper to solve this integration.

Q: Solve: Tanxdy+ y°Sin²xdx=0, y(0)=1 а. у"(3-Сos2x)-2 b. у(-2х + Сos2х) -1 d. y(-1+ Cos2x) — х с. у?…

A: This question is related to differential equations, We will solve it using given information.

Q: Given f"(x) =| 16 sin(4x) and Find f

A:

Q: (1) хdy — ydx — Vx? + у? dx (2) — Зу? — у? sin x dx (3) (x2 + 1)4 — у2 + 1 dy dx

A:

Q: If x'y" + xy'+(x? -y=0 x>0 ,y,=x 2sinx , and y=y,v. Which of the following %3D equations satisfied…

A: Let   y1 and y2be two solutions of the second-order linear differential equation d2ydx2+Pxdydx+Qxy=R…

Q: Let y -2 = S sin³ (t) dt. Use the Fundamental Theorem of Calculus to find y'. ex

A:

Q: Find and of the implicit equatio: a 3x?z + y – xyz' = 0 b ye-* + z sin x = 0,

A:

Q: Suppose that 3x² - y² = t² and y=tsin 0. Find (27). = sin e 0 X = 0 and

A: Given 3x2-y2=t2 and y=tsinθ

Q: (a) If y = xV², then dy dx (b) If y = (2 + sin 3x)", then d (2 + sin 3x)" = T(2 + sin 3x)=-1(cos 3x)…

A: We have to differentiate the given functions: a If y=x2, then dydx=2x2-1 b If y=2+sin 3xπ,then…

Q: Find a particular solution to /" + 16y = 8 sin(4t).

A:

Q: Please

A: We use MOUC to solve given differential equation.

Q: dy cos?x = -(tan x)y ;y(0) = -1 b) Solve %3D dx

A: Given that: dydx-cos2x=-(tanx)y; y(0)=-1

Q: Find the general solution:

A:

Q: y" + 9y = e²* sin(x)

A:

Q: Using Variation of Parameters 4y''-4=cos-1x

A: Given that, 4y''-4=cos-1x Now let's take, 4y''-4=0 Take m=ddx, 4m2-4y=04m2-4=0m=±1 So the homogenous…

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: Solve by variation of parameters method (h) y" + y' = tan x

A:

Q: 4. y=sin(3x) • cos(2x), y'=?

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: ry"+xy'+(x* -y =0 -)y = y = x cosx is a solution of the equation Show that

A: Given               x2y''+xy'+(x2-14)y=0                      (1)

Q: Q2) Find the general solution for this equatio- y" + (tanx-2cotx)y' + (2cot²x)y = 0 If you know that…

A: Given differential equation It has one solution Lets use method of reduction of order.Assume the…

Q: Find the general solution: 2y" + 3y' +y = 2e2 + x² + 3 sin(x).

A:

Q: (#5) ſ cos³ (x)sin*(x)dx =

A: Given the function,

Q: the solution to the given equa y" + y' – 2y = cos(x) – 3 sin(: -

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

Q: (1+x)y' + y = cosx; y(0) = 1

A:

Q: If y(t) is the general solution for the equation: y' + y = sin(t), y(pi/2) = 0 Then, y(0) = ? a)…

A: Consider the differential equation  y'+y=sint,           yπ2 = 0

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.