# Differential equations Questions and Answers

Math

Differential equationsFind the general solution of the given differential equation.
x²y + xy = 4
Give the largest interval over which the general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation)
Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.)

Math

Differential equationsFind an explicit solution of the given initial-value problem.
x2dy/dx = y-xy, y(-1) = -6

Math

Differential equationsConsider the following differential equation and seek a power series solu-
tion centered at ro = 0.
(x²+4)y" - xy + 5y = 0
By putting the equation in standard form, we can see that the radius of
convergence is at least
(A) 2
(B) 4
(C) 5
(D) 6

Math

Differential equationsFind the first four nonzero terms in a power series expansion about x=0 for the solution to the given initial value problem.
w" +5xw'-w=0; w(0)=4, w'(0) = 0

Math

Differential equationsUse implicit differentiation to find the tangent line of the function In(y) = x ln(x) at the point (2,4).

Math

Differential equationsFor the differential equation dy/dx =e-x-3x²:
Part A: Find a general solution. Show all your work.
Part B: Verify the solution. Show all your work.

Math

Differential equationsIf f(x) = 2² +1, use the limit definition of the derivative to compute f'(z). You can use derivative rules to check your answer, but answers calculated without using the definition of derivative will receive very little credit.

Math

Differential equationsSolve the initial value problem x'(t) = Ax(1) for 120, with x(0)=(3,1) Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described by x¹=Ax. Find the directions of greatest attraction and/or repulsion
2 -4
6-8

Math

Differential equations5. Consider differential equation
dy/dx + (2/x) y = xy³, y(1) = 1/2
Find y(10) numerically using the following methods and h = 0.5, 0.25, 0.125 and calculate
the errors in each case. You have to use MATLAB for this problem. (10 Points each)
a. Forward Euler's method
b. Backward Euler's method
c. Modified Euler's method
d. Improved Euler's method
e. Fourth-Order Runge Kutta Method

Math

Differential equationsA jogger runs around a circular track of radius 65 ft. Let (x, y) be her coordinates, where the origin is the center of the track. When the jogger's coordinates are (39, 52), her x-coordinate is changing at a rate of 16 ft/s. Find dy/dt.
dyldt = ft/s

Math

Differential equationsThe rate of change of the number of raccoons N(t) in a population is directly proportional to 380 N(t), where t is the time in years. When t = 0, the population is 120, and when t = 4, the population has increased to 160. Find the population when t = 8.
(Round your answer to the nearest integer.)
raccoons

Math

Differential equationsGiven the sets of system linear of differential equation;
2x"+6x'+y" + 3y' = 12e ^-t
x'+2x + y' = 0
(a) Determine x(t) by using Elimination Method.
(b) Determine y(t).
(c) Check number of arbitrary constant and determine the final solutions.

Math

Differential equationsIn drawing the slope field for the differential equation dy/dx= x+3y-4, I would draw a short line segment for different points on the x-y plane.
What slope should I draw the line segment at the point (0,-2)?
Your Answer:

Math

Differential equationsSolve the differential equation, such that the equation passes through the given point (x, y). (Remember to use absolute values where appropriate.)
dy/dx = 5/x (1, 2)
y = log(x5) +2

Math

Differential equationsConsider the autonomous first-order differential equation dy/dx = y - y³ and the initial condition y(0) = y₀. Sketch the graph of a typical solution y(x) when y₀, has the
given values.
(a) y₀ > 1

Math

Differential equationsA 4-kg object's position, p, is changing with respect to time, t. The object experiences a force, F, that is proportional to the object's acceleration times its mass. What differential equation represents this dynamic?
A. F = 4p'
B. F = 4p"
C. F = 4v
D. F = 4t