A mass of 1 slug is attached to a spring whose constant is 5 lb/ft. Ini- tially the mass is released 1 ft below the equilibrium position with a downward velocity of 5 ft/s, and the subsequent motion takes place in a medium that offers a damping force numerically equal to 2 times the instantaneous velocity. Find the equation of motion if the mass is driven by an external force equal to f(t)= 12 cos 2t + 3 sin 2t. transient solutions.

Q: dy 2ry = 1+ y? , y(2) = 3 da

A:

Q: (c) L¹{In( S -)} T+₂S

A:

Q: What is the degree of homogeneous differential equation (x+y)dx + x² + y² dy? А. 1 В.2 С.3 D. 0

A: Given differential equation is of the form       M(x,y)dx+N(x,y)dy   So we assume…

Q: dr ᎾᏢ sin 0 - r- cos e eo +- cos = 0

A:

Q: ex dx-y? dy=

A:

Q: "s" is what kind of number?

A:

Q: For the line that has the equation X1 + 2X2 = 10, will pass through: %3D O (5,4) (10,1) O (2,4) O…

A: Given that  The equation of a line is x1+2x2=10 To find a point that will pass through the given…

Q: Subject: Differential Equations y" – 3y' + 2y = 2x? (D2 – 5D + 4)y = 4x 1. 2.

A:

Q: HIGHER ORDER OF DIFFERENTIAL EQUATIONS (D⁵ + D⁴ - 7D³ - 11D² - 8D - 12)y = 0 Pls show complete…

A:

Q: solution of differential equations in terms of bessel function

A:

Q: Subject: Differential Equations 1. y" – 2y' +y = x³ +1

A:

Q: State the linearity and order of the differential equation t -()"+ 0. de

A:

Q: 6. -4s 2 S

A:

Q: . Exercise 1.3 Solve 1. (x+2)²y" + (x+2)y -y=0

A:

Q: 3 Obta in the gencral solution (o"-D'- 70° +D tG)y

A:

Q: “些。 de e +1 dr

A: Here we will use separation of variable method.

Q: 2. Working with convolutions: a. Find t * cosh t b. Find L{t* cosh t}

A:

Q: Answer true or false. The function f(t) = (et) 10 is of exponential order. O True O False

A: We have to determine that whether the function,  f(t) = et10 is of exponential order or not.

Q: Let A- ] and ů = (3) %3D %3D Commpute Av Solve for x 2-x det 10 1- X

A: Use matrix multiplication, to calculate Av⇀. Av⇀=2310113=21+33101+13=2+910+3=1113 Therefore,…

Q: F(s) means Your answer

A: Using the definition of Laplace transform.

Q: 4. Solve (D² -1)y =(x'+2x² + x +6)e²* using differential operators method.

A: Let us consider differential equation: ay''+by'+cy=f(x) Write auxiliary equation to get…

Q: Gy" dx -x(2x? +y)dy-0

A: First make it as in the  form of bernouilli equation  then  simple find the integrating factor then…

Q: dy dr + y = x

A: We are asked to find the degree of the differential equation.

Q: 1) What is the equation of the circle whose diameter has endpoints P(1, 6) and Q(7, 2)? Center: (…

A:

Q: (x+y) dx = (²x y J J y so

A: