seconds is given by S(t) = 6t - 28t mete quals 0. [0.

Q: After the medical breakthrough, So(t) =1 0<t<w. Calculate w.

A: Solution

Q: (c) -7x+12x = 2 given that at t 0, x 1 and i 5

A:

Q: Solve the following 2nd order D.E: y'' + 2 y' = x^2-e^x

A: given ,         differential equation,   y''+2y'=x2-ex

Q: Q4: Solve the following O.D.E: (x² + y²) ý = xy with the initial condition y(1) = 2, on the interval…

A:

Q: If we wish to solve u′(t)=1−u(t),u(2)=2 up to tf=4 by using 5 subintervals, then u(t2)= . This…

A:

Q: Find the general solution to y"(t) = t1² – 3t* + e' – nsin (at). Show all steps

A: y"(t)=t12-3t4+et-πsin(πt)d2ytdt2=t12-3t4+et-πsin(πt)

Q: Q12: What is the formula of The general solution for a D.E. with variable coefficients about…

A: Given x0 is an ordinary point of the differential equation.

Q: Solve the D.E t²y" - 2y = 0, given that y1(t)= t² is a sol'n.

A:

Q: Show that g(t) = t / ( t+1 ) takes on the value 0.499 for some tin [0, l].

A: To show that g(t)=tt+1takes on the value 0.499 for some t in [0, 1]. We use intermediate value…

Q: Find a general solution to the given equation for t<0. (t^2)y''(t)-5ty'(t)+15y(t)=0

A:

Q: If C = 100, k = 0.1, and t is time in minutes, how long will it take a hot cup of coffee to cool to…

A: From Newton’s Law of Cooling, we know that T(t) = Ts + Cekt Given C = 100, k = 0.1 Consider freshly…

Q: Q2/A) Find the particular solution for the following D.E., the boundary condition is (y-0 @x-0) dy =…

A:

Q: 5. Show that 1 T = VI? + y? satisfies the equation Tz + Tyy = T3

A: Given T(x,y)=1x2+y2

Q: Q3) Use Euler's method to estimate y(0.02) ey-x y' 1+ e2y •y(0) = 2 (h=0.01) .What is the error in…

A:

Q: For y''+3y'+2y=e^-x, use the variation of parameters formula to find a particular solution. Show…

A:

Q: Determine the Solution of the following D.E.: (2) xydx + 2(x2 +2y²)dy D0; when x=0, y= 1

A:

Q: Q4: Solve the following O.D.E: (xy)ý = (x2 + y²) with the initial condition y(1) = 1, on the…

A:

Q: A particle with velocity at any time t given by v(t)=e't moves in a straight line. How far does the…

A: solve the following

Q: Q2. If the solution of the below first order D.E is y = Cefxy) (x + xy?)y' = y3 Find the f(x, y).

A:

Q: 13. Solve the DE t'y" – 3ty' + 4y = 0, t > 0

A:

Q: The position of the particle at time t is given by s(t) = t2 – 9t + 8. The particle is rest at…

A:

Q: Approximate the value(s) of x that satisfies the equation lnx =x2 −1.

A: The given equation is: lnx=x2-1 To find the approximate value of x that satisfies the given…

Q: (i) A business manager determines that t months after production begins on a new product, 6t2 + 5t…

A: Given: P(t) = 6t2 + 5t(t + 1)2 To Find: limt→∞P(t).

Q: The position of the particle at time t is given by s(t) = t² – 6t + 8. The particle is moving from…

A:

Q: 4y"-y=e^x/2+6 consider the following DE to be solved by variation of parameters

A:

Q: Q2. If the solution of the below first order D.E is y = C ef9) (+xy)y=y Find the f(x, y).

A:

Q: Consider the IVP y'= -y + t + 1 with y(0) = 1, for t e [0, 5]. What is the corresponding Lipschitz…

A:

Q: Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a)…

A: As this problem is related to vector differential equation of a matrix, hope you know how to find…

Q: For a t-curve with df = 11, find the t-value to 10: O A. 1.280 ОВ. 1.363 O C. 2.718 O D. 1.372

A: Given Degrees of freedom (df)=11

Q: dy Solve the initial-value problem for y as a function of 2. (64 – x²) - 1, y(0) = 6 dr y =

A:

Q: If the power of the rocket handler is given by [(t – 11)(t² + 1) + 5(7t – 5)]e-0.5t Where t is the…

A:

Q: Show steps please.

A:

Q: Solve the following 2nd order D.E using variation of parameters method: y'' + 2 y' + y = e^(-x)

A: The non homogeneous differential equation is given as y''+2y'+y=e-x Corresponding homogeneous…

Q: The position of a particle moving along the x - axis at time t is given by x(t) = ecos2t, 0<ts . For…

A:

Q: Using the initial condition y(0) = 3, we find y(0) = −e0 + C = 3, so C = 4. Thus, y(x) = 4 − e−x .…

A: To find f'(t) we integrate  c=integrating constant  Given f'(0)=-1 , using that we find c

Q: The number N(t) of supermarkets throughout the country that are using a computerized checkout system…

A: The number N(t) of supermarkets throughout the country that are using a computerized checkout system…

Q: solve the following D.E ,t<3 y" – 3y - 4y =- , y(0) = 0, y'(0) = 0 : ,t23

A: Here we will use Laplace transform method to solve the given differential equation.

Q: Use the method of variation of parameters to solve the following y + 4y + 4y e- In z, z>0

A:

Q: For a t-curve with df = 11, find the t-value to 10: O A. 1.280 В. 2.718 O C. 1.363 O D. 1.372

A:

Q: Q2. If the solution of the below first order D.E is y = C el(x.y) (x' + xy?)y' = y³ Find the f(x,…

A: Given that The solution of th given D.E. is  y=Ce^f(x,y)

Q: Solve the following problem by using the KKT conditions P : Min er²+y² s.t. 2x – y = 4.

A: To find - Solve the following problem by using the KKT conditions                  P : Min ex2 +…

Q: Solve the 2nd order D.E. below using method of undetermined coefficients : y''+ 7 y' = 42 x^2 + 5x…

A: To find the solution, first, solve the homogenous ODE, y''+7y'=0 and obtain yh=C1+C2e-7x.…

Q: Solve the problem. At time t > 0, the velocity of a body moving along the s-axis is v-2-7t+6. When…

A: The objective is to find when the velocity of the body is increasing.

Q: Find the solution for the following ODE; y2 - y' = 0 with the initial condition  y(6) = 3 What is…

A:

Q: Find the value of k so that the value of (2y - 1) dy is 10.

A:

Q: If the power of the rocket handler is given by P = [(t – 11)(t² + 1) + 5(7t – 5)]e¬0.5t Where t is…

A: To find the energy we take the integral of the given power function between t=1 and t=4.…

Q: Given d'y dx² = 6x-0.5x², y(0) = 0, y(12)=0, Use step size h = 4, z1 = 20, and z2 = 25. Enter 4…

A:

Q: Suppose a person wants to travel D miles at a constant speed of (60 + x) mi/hr, where x could be…

A: Given that speed is  s=(60+x) mi/hour time required to travel D miles is T(x)=60D(60+x)-1 in minutes

Q: Solve the following initial value problem for  y = f (x). dy dx  =  e−3x, y = 79  when  x =…

A: dydx=e-3x and y=79 whrn x=0