f'(x) = -6f(x), and f(2) = 1. Solve the equation. 选择一项: a. f(x) = 2e¬× b. f(x) = e12-6x c. f(x) = –12e-6x d. f(x) — е-бх = e

Q: Find the number of units sold that yields a maximum annual revenue for a sporting goods…

A:

Q: Solve the DE f(x) 5x given that f(0) = 3. O y=+15 A x² + 15 O y=-3 5 x2. B © v=-15 극x2-15 (c) c y= D…

A:

Q: Water is leaking from a tap at a rate of x cm³/min. (a) Write down an expression for the time taken…

A:

Q: Calculates  ∫ln(x2+bx+c) note: 4c−b2<0.

A: Consider the given integral   Find the integration of first team,

Q: A mountain climber feels that the air temperature decreases as his elevation increases. When his…

A:

Q: (a) Form the difference equation whose solution is yk = c1 + (c2+ csk)(-1)*, where c1, cz and cs are…

A: Given that the solution is yk=c1+c2+c3k-1k. To find the difference equation of this solution: For,…

Q: Solve 2, y(0) = 22 - -58 - 15 x(t) =

A: Given,          x'y'=52-58-15xy,   x(0)=-2, y(0)=22

Q: (2x² - x - 1) x³ - x² ; 2 dx

A:

Q: A ball is thrown downward with a speed of 11 ft/s from the top of a 121-foot-tall building. After t…

A:

Q: R(x) = -.722x3 + 19.23x2 - 161.2x + 421.8, where x = 6 corresponds to the year 2006.  (a) What was…

A:

Q: Solve: dy = (x – 3y) dx %3D xt = (3t2 + c)e2t b. 9y = 3x – 1+ ce-3x %3D -3ex + x3y C = 0 +e + a.

A: Given that: dy=(x-3y)dx

Q: Use the substitution ux)%3D2х - Зу (x)+2 to solve the following IVP: У'+ (2х - Зу +2)23D0, у (0) —2

A: Given that diffrancial equation y'+2x-3y+22=0  , y0=2Solutiondydx=-2x-3y+22let…

Q: Enter the solution to the equation f(x)-g (x) = 0

A: Here we find solutions for f(x)-g(x) = 0

Q: The windchill index announced during the winter by the weather bureau measures how cold it "feels"…

A:

Q: x3y'''+2x2y''-2xy'=2x-4 Find the general solution of the equation.

A:

Q: Solve the diff eq (ху?+x-2у+3)dx +(x?у — 2х - 2у)dy %3D0

A:

Q: If the initial velocity of a projectile is 96 feet per second, then its height in feet is a function…

A: Approach to solving the question:Please see attached photos for detailed solutions. Thank you.…

Q: (D²-1)y = x-1, solve using Method of Undetermined Coefficient. %3D

A:

Q: (x5+2x² + 1)dx x3 x³ - x

A: We know that integration of xn  is- xn+1/n+1 + C . Here C is integral cosntant.   Here i attached…

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: Solve y(2) + y = csc² x by Variation of parameter

A:

Q: Solve for ‘x’ and ‘y’:(a – b) x + (a + b) y = a2 – b2 – 2ab(a + b) (x + y) = a2 + b2

A: Given,

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.