Question

Verify that all members of the family *y* =
(2)^{1/2} (*c* -
*x*^{2})^{-1/2} are solutions of the
differential equation

Find a solution of the initial-value problem. y' = (xy^3)/2 , y(0) = 9

Answer #1

Given that

The given differential equation is

Substituting the values x = 0 and y = 9 in the given family of functions, we get

Hence, the solution of the initial-value problem y' = (xy^3)/2 , y(0) = 9 is

(a) Verify that all members of the family y =
(6)1/2 (c -
x2)-1/2 are solutions of the
differential equation.
(b) Find a solution of the initial-value problem.

(a) Verify that all members of the family y =
(2)1/2 (c -
x2)-1/2 are solutions of the
differential equation.
(b) Find a solution of the initial-value problem.
y(x) is what

(a) verfiy that y=tan(x+c) ia a one parameter family of
solutions of the differential equation y'= 1+x^2
(b)since f(x,y)= 1+y^2 and df/dy= 2y are continuous everywhere,
the region R can be taken to be the entire xy-plane. Use the family
of solutions in part A to find an explicit solution of the first
order initial value problem y'= 1+y^2, y(0)=0. Even though x0=0 is
in the interval (-2,2) explain why the solution is not defined on
its interval
(c)determine the...

Verify that the function
y=x^2+c/x^2
is a solution of the differential equation
xy′+2y=4x^2, (x>0).
b) Find the value of c for which the solution satisfies the initial
condition y(4)=3.
c=

Verify that the equation y = x2+ 2x+2+Cex
is a solution to the differential equation
y'-y+x2=0.

In this problem,
y = c1ex + c2e−x
is a two-parameter family of solutions of the second-order
DE
y'' − y = 0.
Find a solution of the second-order IVP consisting of this
differential equation and the given initial conditions.
y(−1) = 7, y'(−1) = −7

In this problem, y = c1ex +
c2e−x is a two-parameter family of
solutions of the second-order DE y'' − y = 0.
Find a solution of the second-order IVP consisting of this
differential equation and the given initial conditions.
y(−1) = 8, y'(−1) = −8
y=

(a) Use the fact that 5x2 − y2 = c is a one-parameter family of
solutions of the differential equation y dy/dx = 5x to find an
implicit solution of the initial-value problem y dy/dx = 5x, y(4) =
−10.
Then sketch the graph of the explicit solution of this
problem.
Give the interval I of definition of the explicit
solution. (Enter your answer using interval notation.)
(b) Are there any explicit solutions of y dy/dx =
5x that pass through...

1) ?1(?) = 5 , ?2(?) = sin2 ? y ?3(?) = cos2 ? (−∞,∞) it is
linearly dependent or independent.
2)Determine the Wronskian of the Function Set
?1(?) = ?2 y ?2(?) = 1 − ?2, ?3(?) = 2 + ?2 (−∞,∞)
3) Be a solution of the differential equation?2?′′ − 3??′ + 5? =
0
Find a second solution using the order reduction formula.
4) Find the general solution of the differential equation.
?′′′ + 3?′′...

3. Consider the differential equation: x dy/dx = y^2 − y
(a) Find all solutions to the differential equation.
(b) Find the solution that contains the point (−1,1)
(c) Find the solution that contains the point (−2,0)
(d) Find the solution that contains the point (1/2,1/2)
(e) Find the solution that contains the point (2,1/4)

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