Question

Solve the given initial value problem and determine at least approximately where the solution is valid.

(12x^{2}+y−1)dx−(18y−x)dy=0, y(1)=0

y= ,

the solution is valid as long as ≥0

Answer #1

Solve the given initial value problem and determine at least
approximately where the solution is valid. (6x2+y−1)dx−(6y−x)dy=0,
y(1)=0
y= ????? , the solution is valid as long as _____>=0
PLEASE help me and make sure it is in the format y=, and please
explain how. Thank you.

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 initial value problem and determine the interval in
which the solution is valid. Round your answer to three decimal
places.
y′=6x^2/(6y^2−11), y(1)=0
2y^3=2x^3+11y-2
The solution is valid for (fill in the blank)<x<(fill in
the blank)

Consider the initial value problem
dy/dx= 6xy2 y(0)=1
a) Solve the initial value problem explicitly
b) Use eulers method with change in x = 0.25 to estimate y(1)
for the initial value problem
c) Use your exact solution in (a) and your approximate answer in
(b) to compute the error in your approximation of y(1)

Solve the given initial-value problem. (x + 2) dy dx + y =
ln(x), y(1) = 10 y(x) =
Give the largest interval I over which the solution is defined.
(Enter your answer using interval notation.)
I =

Solve the given initial-value problem by finding, as in Example
4 of Section 2.4, an appropriate integrating factor. (x2 + y2 − 7)
dx = (y + xy) dy, y(0) = 1

19. Solve the initial value problem and determine where the
solution attains its maximum value. Please use good handwriting and
show as many steps as possible.
y'= 2cos(2x)/(3+2y), y(0)= -1

Solve the 1st-order linear differential equation using an
integrating fac-
tor. For problem solve the initial value problem. For each
problem, specify the solution
interval.
dy/dx−2xy=x, y(0) = 1

Solve the initial value problem y′=[10cos(10x)]/[3+2y], y(0)=−1
and determine where the solution attains its maximum value (for
0≤x≤0.339). Enclose arguments of functions in parentheses. For
example, sin(2x).
y(x)=
The solution attains a maximum at the following value of x.
Enter the exact answer.
x=

Solve for Y(s), the Laplace transform of the solution y(t) to
the initial value problem below. y''-9y'+18y=5te^(3t), y(0)=2,
y'(0)=-4

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