Interpret the statement as a differential equation. (Use yp for y' and ypp for y".)
Interpret the statement as a differential equation. (Use yp for y' and ypp for y".)
On the graph of y = φ(x), the rate at which the slope changes with respect to x at a point P(x, y) is the negative of the slope of the tangent line at P(x, y).
Homework Answers
slope of the tangent at P(x,y)
rate at which slope changes with respect to x at P(x,y)
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Interpret the statement as a differential equation. (Use yp for y' and ypp for y".)
Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation...
Use the substitution
x =
et
to transform the given Cauchy-Euler equation to a differential
equation with constant coefficients. (Use yp for
dy
dt
and ypp for
d2y
dt2
.)
x2y'' +
7xy' − 16y = 0
Use the substitution x = ef to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use yp for dy and ypp for dt dt2 x?y" + 7xy' - 16y = 0 x Solve the original equation by solving the...
Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation...
Use the substitution
x = et
to transform the given Cauchy-Euler equation to a differential
equation with constant coefficients. (Use yp for
y
dt
and ypp for
d2y
dt2
.)
x2y'' − 3xy' + 13y = 4 + 7x
Solve the original equation by solving the new equation using
the procedure in Sections 4.3-4.5.
Use the substitution X = e' to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use yp for- and ypp for t...
Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation...
Use the substitution
x =
et
to transform the given Cauchy-Euler equation to a differential
equation with constant coefficients. (Use yp for
dy
dt
and ypp for
d2y
dt2
.)
x2y'' +
10xy' + 8y =
x2
Solve the original equation by solving the new equation using the
procedures in Sections 4.3-4.5.
y(x) =
Use the substitution x = ef to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use yp for dy and ypp for...
Consider the differential equation dy/dx = (y-1)/x.
Consider the differential equation dy/dx = (y-1)/x. (a) On the axes provided, sketch a slope field for the given differential equation at the nine points indicated. (b) Let y = f (x) be the particular solution to the given differential equation with the initial condition f (3) = 2. Write an equation for the line tangent to the graph of y= f (x) at x = 3. Use the equation to approximate the value of f (3.3). (c) Find the particular solution y...
Consider the differential equation dy dt = t - 2 According to the differential equation, what...
Consider the differential equation dy dt = t - 2 According to the differential equation, what is the value of y (0)? Question 3 Consider the differential equation dy dt = t - 2 and the given information y(0) = 1. Select the figure that shows the correct graphical representation of y' (O). 0 O 3 y 21 + -2 y 2 1 2 1 2 A z -1 O 3 y 2 X 2. z -1 O 3 2+...
17. Consider the differential equation given by dy/dx = xy/2
17. Consider the differential equation given by dy/dx = xy/2 (A) On the axes provided, sketch a slope field for the given differential equation. (B) Let f be the function that satisfies the given differential equation. Write an equation for the tangent line to the curve y (x) through the point (1, 1). Then use your tangent line equation to estimate the value of f(1.2) (C) Find the particular solution y=f(x) to the differential equation with the initial condition f(1)=1. Use your solution...
Maple program what are the commands Question6 For the following equation y't y P (0,1) a) Plot the equation with the implicitplot command. Check to see that the given b) Using the implicitd...
Maple program what are the commands
Question6 For the following equation y't y P (0,1) a) Plot the equation with the implicitplot command. Check to see that the given b) Using the implicitdiff command, find a formula for the derivative and find c) point P satisfies the equation the slope at the given point P Use the slope found in part (b) to find an equation for the tangent line to the curve at P. Then plot the equation together...
The variables x and y are implicitly related to the equation x^4+ { ^Y down 1...
The variables x and y are implicitly related to the equation x^4+ { ^Y down 1 e^-t^2 dt =1 ( Y is at the top of the { and 1 is at the bottom of the { ) The point p=(1,1) lies on the graph of the equation. Find the slope of the line tangent to the graph at the point p=(1,1) A.) 2e^-2 B.) 2e C.) -4e D.) -4e^-1 E.) 4e^-2
y = 3x0+ QUESTION 2 Solve the given differential equation. (The form of yp is given...
y = 3x0+ QUESTION 2 Solve the given differential equation. (The form of yp is given D2y + 25y = -5 sin 5x (Let y p = Ax sin 5x + Bx cos 5x.) sin 5x + c2 cos 5x + x sin 5x - 1 x cos 5x Oo oo cos 5x + = x cos 5x y = C1 sin 5x + C2 cos 5x + 5x sin 5x y = C1 sin 5x + C2 cos 5x...
Graph the equation and its tangent.
Graph the equation and its tangent. a) Graph y = x3 - 4 and the tangent to the curve at the point whose x-coordinate is 0 and the tangent line to the curve at the point whose x-coordinate is 0. b) What is the equation of the tangent line at x = 0 in slope-intercept form (i.e. y = mx+b)?
Use the substitution
x =
et
to transform the given Cauchy-Euler equation to a differential
equation with constant coefficients. (Use yp for
dy
dt
and ypp for
d2y
dt2
.)
x2y'' +
7xy' − 16y = 0
Use the substitution x = ef to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use yp for dy and ypp for dt dt2 x?y" + 7xy' - 16y = 0 x Solve the original equation by solving the...
Use the substitution
x = et
to transform the given Cauchy-Euler equation to a differential
equation with constant coefficients. (Use yp for
y
dt
and ypp for
d2y
dt2
.)
x2y'' − 3xy' + 13y = 4 + 7x
Solve the original equation by solving the new equation using
the procedure in Sections 4.3-4.5.
Use the substitution X = e' to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use yp for- and ypp for t...
Use the substitution
x =
et
to transform the given Cauchy-Euler equation to a differential
equation with constant coefficients. (Use yp for
dy
dt
and ypp for
d2y
dt2
.)
x2y'' +
10xy' + 8y =
x2
Solve the original equation by solving the new equation using the
procedures in Sections 4.3-4.5.
y(x) =
Use the substitution x = ef to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use yp for dy and ypp for...
Consider the differential equation dy dt = t - 2 According to the differential equation, what is the value of y (0)? Question 3 Consider the differential equation dy dt = t - 2 and the given information y(0) = 1. Select the figure that shows the correct graphical representation of y' (O). 0 O 3 y 21 + -2 y 2 1 2 1 2 A z -1 O 3 y 2 X 2. z -1 O 3 2+...
Maple program what are the commands
Question6 For the following equation y't y P (0,1) a) Plot the equation with the implicitplot command. Check to see that the given b) Using the implicitdiff command, find a formula for the derivative and find c) point P satisfies the equation the slope at the given point P Use the slope found in part (b) to find an equation for the tangent line to the curve at P. Then plot the equation together...
y = 3x0+ QUESTION 2 Solve the given differential equation. (The form of yp is given D2y + 25y = -5 sin 5x (Let y p = Ax sin 5x + Bx cos 5x.) sin 5x + c2 cos 5x + x sin 5x - 1 x cos 5x Oo oo cos 5x + = x cos 5x y = C1 sin 5x + C2 cos 5x + 5x sin 5x y = C1 sin 5x + C2 cos 5x...
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