The velocity of a particle moving in a straight line is given by v = e³r + 31. Find an expression for the position s after a time t. O a. s(t)= e3+3r² + C O b. s() =*+ 6r° +C O. s(t) = 3e³t + 3+C O d. s() =*++c O e. s()=*++c

Q: O Solve y' = x + y + xy, y(0) = 1 by choosing step length 0.2 for y(0.4) by Euler's modified ethod

A: Given y'=x+y+xy, y(0)=1 Take f(x,y)=x+y+xy, Using the euler formula, Since it is given that h=0.2.…

Q: 2. Eliminate the arbitrary constant on the given equation: y = C₁e-²x + De4x

A: Given  y=C1e-2x+De4x

Q: The position of a body moving along s-axis at any time 't' is given by s(t) = 9t3 – 48t, then the…

A:

Q: The profit P(x) pesos from producing r thousands of goods is given by P(r) = 11r² + 1980r + k for…

A: Given that the profit pesos from producing “x” thousands of goods is given by, Px=11x2+1980x+kWhere…

Q: The velocity of a particle, in feet per second, is given by v = t 2 - 3t + 9, where t is the time…

A:

Q: An insect is in a toxic environment. The level of toxicity is given by T(x,y)= 2x* – 4y° If the…

A: Tx=0⇒x=0Ty=0⇒y=0Using D-TestD=TxxTyy-[Txy2]D=0 at (0,0)   T(x,y) is minimum

Q: A particle that moves along a straight line has velocity v ( t ) = t 2 e − 5 t v ( t ) = t 2 e - 5 t…

A: →v(t) = ds(t)dt→Use integration by parts.

Q: ty (t+1)y + y = t²

A: Given That : ty"-(t+1)y'+y=t2 To find: solve the differential equation using determinant coefficient…

Q: A ball is tossed off a tower 288 feet high and its position, s, at time t, in seconds is given by…

A: Solve it in two parts part 1 when ball reaches at height of 288 feet again  we calculate time to…

Q: The position of a particle travelling along a horizontal line in t seconds is s(t) = 2t3 – 12t2– 72t…

A: The position of a particle is given by the equation is: st=2t3-12t2-72t+7. Then, velocity of the…

Q: Solve for the General Solution of the given first-ordered Lineor DE : X lx² +1)y'+2y= (x?+1) %3D

A:

Q: O': what is the general solution of the equation. dy dr xy

A:

Q: A SERIES ELECTRICAL CIRCUIT WHICH YOU ARE TESTING FEATURES A CAPECTIOR (C) CHARGING VIA A IMS…

A: Resistance =1M ohm=10⁶ ohm Dc supply =12V Voltage across capacitor = 2V  Time = 4sec

Q: 2. Solve dx2 d²y for x = u? + 1 and y = 3u3 – 3u in terms of the parameter u. -

A: Given query is to find indicated derivative.

Q: An airplane is flying at 320 km/h due south and encounters a wind from [S 40° W] at 70 km/h. Find…

A: Given  An airplane is flying at 320 km/h due south and encounters a wind from [S 40° W] at 70 km/h.

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: A particle moves along the x-axis with the origin as the reference point so that at time t in…

A: Recall what Newton said to us: Velocity = rate of change of position Hence, v(t) = dx/dt

Q: Use the explicit Euler method to plot the  estimate y(2) if y(t) is the solution to y' = t - y3 with…

A: Given IVP is y'=t-y3, y(0)=1 we have  f(t,y)=t-y3 Here using n=10 steps, Then step size h=upper…

Q: Q2. A particle moves along a straight line so that aftert (seconds), its distance from Oa fixed…

A:

Q: Use variation of parameters to find the particular solution to 3t y'' + 5y + 4y = 2e Y(t)=| Preview

A:

Q: The velocity of a moving particle at any time t is given by expression 12t2 + 10t +7. If when t =…

A:

Q: A particle moves on the x-axis with velocity given by v(t) = 3t4 − 11t2 + 9t − 2 for −3 ≤ t ≤ 3 .…

A:

Q: Use variation of parameters to find the particular solution to y'' + 5y' + 4y = 2e-34 Y(t) = […

A:

Q: Use variation of parameters to find a particular solution of 14aie" 3 y" – 2y' + y - Yp(x)

A:

Q: 4. A certain particle is travelling in a straight line governed by the equation a = v5 m / s?. If…

A: we know the first equation of motionv=u+atv=1+2v95  m/s

Q: The position of a particle moving along a coordinate axis is given by s(t)=t^3−9t^2+24t+4 for t≥0.…

A: For velociti differentiation of position vector And for acceleration derivative of velocity vector

Q: Find the general solution to the DE using the method of Variation of Parameters 8 y" – 4y = e2x + 1

A:

Q: Q3) Use Euler's method to estimate y(0.02) ey-x y' =- 1+e2y „y(0) = 3 (h=0.01) .What is the error in…

A: According to Euler's method: yn+1=yn+hf(xn,yn), where xn+1=xn+h and h is a considered step size.…

Q: The displacement (in meters) of a particle moving in a straight line is given by s= t2 - 5t + 16,…

A: We want to find average velocity.

Q: Suppose that a particle moves along a line with position function s(t) =2t^2 +3t+1 where s is in…

A:

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

A:

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

A:

Q: Find the value of d2y/dx2 at the point defined by the given value of t. x = t, y = square root 2t ,…

A:

Q: Grass clippings are placed in a bin, where they decompose. For 0 sts 10 , the amount of grass…

A: First find the Linear approximation function of the A(t) then solve the problem.

Q: (D* – 4D³ +14D² – 20D +9)y = 0 - -

A:

Q: A particle moves in a straight line such that its acceleration when at position (with respect to a…

A: Given: a=x3+4, v0=11 The objective is to calculate the velocity function v of the particle when at…

Q: A particle moving in a straight line covers a distance of x cm in t second, where x = t³ + 6t² − 15t…

A: Solution is given below

Q: If s = 3t2 – 16t¯², when will - acceleration be zero? An object moves along a horizontal line…

A: To find  When acceleration will be zero.

Q: A particle moves along the x-axis so that at time t≥0 its position is given by x(t)=2t3+3t2−36t+50.…

A: given, A particle moves along the x-axis so that at time t≥0 its position is given by…

Q: A particle moves along the x-axis with velocity given by v(t) = 3t2 + 13 for time t > 0. If the…

A:

Q: Suppose that the displacement of a particle at timet in seconds is given by s(t) = + 5t2. Which of…

A:

Q: The velocity of a particle moving on a straight line is given by v(t) = t^2e^-t meters per second at…

A:

Q: Consider a particle with a position function given by s(t)=48t-3t^2. When will the the particle…

A:

Q: A particle moving on a line is at position x(t)=t3−9t2+24t−5 at time t where t is in seconds. At…

A: The given function for position of an object is where t is the time in seconds. Now, to find points…

Q: An insect is in a toxic environment. The level of toxicity is given by I(x,y)= 2x* – 4y If the…

A:

Q: A particle moves in a straight line according to the law equation of motion s = t2 – 20t + 20  where…

A: s = t2 – 20t + 20dsdt represents velocity of the particle hence when particle stop velocity will be…

Q: (a) Find the velocity of the particle at time t. s'(t) = (b) When is the velocity 0? (Use n as the…

A: Follow the procedure given below.

Q: Q3- Choose the correct answer: 1-If velocity of a particle is given 4 points by v = 10 + 2t2 m/s,…

A: If velocity of a particle is given by v=10+2t^2 m/s. the average acceleration between 2 and 5s is…

Q: The velocity of a particle moving along the x-axis is v(t) = 5t² – 4t + 2 and the particle passes…

A: Solution and Explanation is given below.....

Q: 7. A swimmer orients herself perpendicular to the parallel banks of a river. If the swimmer's…

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.