Question

find the particular solution for the following initial value problems

A) x dy/dx +2y = x to the power of 2 +x , y(1)=1

Answer #1

Solve the initial value problems.
1) x (dy/dx)+ 2y = −sinx/x , y(π) = 0.
2) 3y”−y=0 , y(0)=0,y’(0)=1.Use the power series method
for this one . And then solve it using the characteristic
method
Note that 3y” refers to it being second order
differential and y’ first

Consider the initial value problem
dy dx
=
1−2x 2y
, y(0) = − √2
(a) (6 points) Find the explicit solution to the initial value
problem.
(b) (3 points) Determine the interval in which the solution is
deﬁned.

Find the general solution and initial value solution: (cos x)dy
= -2y2(tan x)dx, y(0)=1/6

Find a particular solution to each of the following differential
equations with the given initial condition:
A) dy/dx=ysinx/1+y^2, y(0)=1
B)dy/dx=xy ln x, y(1)=3
C)xy(1+x^2) dy/dx=(1+y^2), y(1)=0

Initial value problem : Differential equations:
dx/dt = x + 2y
dy/dt = 2x + y
Initial conditions:
x(0) = 0
y(0) = 2
a) Find the solution to this initial value problem
(yes, I know, the text says that the solutions are
x(t)= e^3t - e^-t and y(x) = e^3t + e^-t
and but I want you to derive these solutions yourself using one
of the methods we studied in chapter 4) Work this part out on paper
to...

Consider the system [ x' = -2y & y' = 2x] . Use dy/dx to
find the curves y = y(x).
Draw solution curves in the xy phase plane. What type of
equilibrium point is the origin?

In the following problems determine whether existence of at
least one solution of the
given initial value problem is thereby guaranteed and if so,
whether the uniqueness of
that solution is guaranteed. For each initial value problem
determine all solutions and
the intervals where they hold, if the case.
(a) dy/dx = y^(1/3); y(1) = 1.
(b) dy/dx = y^(1/3); y(1) = 0.
(c) dy/dx =sqrt(x - y); y(2) = 1.
Can you explain how can we approach these kind...

Solve the following DE:
x dy/dx + 2y = x^2 - x + 1 ; y(1) = 1/2

1.Solve the following initial value problem
a) dy/dx= y2/(x-3), with y(4)=2
b) (sqrt(x)) dy/dx = ey+sqrt(x), with y(0)= 0
2. Find an expression for nth term of the
sequence
a) {-1, 13/24, -20/120, 27/720, ...}
b) {4/10, 12/7, 36/4, 108, ...}

Solve the following ODE's/ IVP's
y'=1/xsin(y)+2sin(2y)
Hint: consider x=x(y) and dx/dy=1/(dx/dy)=1/y'

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