Question

Determine whether the equation is exact. If it is exact, find the solution. If it is not, enter NS.

(y/x+7x)dx+(ln(x)−2)dy=0, x>0

Enclose arguments of functions in parentheses. For example, sin(2x).

Answer #1

Determine whether the equation is exact. If it is exact, find
the solution. If it is not, enter NS.
(4x2−2xy+5)dx+(5y2−x2+4)dy=0

Find the solution of the initial value problem
y′′+4y=t2+7et y(0)=0, y′(0)=2.
Enter an exact answer.
Enclose arguments of functions in parentheses. For example,
sin(2x).

Determine whether the given differential equation is exact. If
it is exact, solve it. (If it is not exact, enter NOT.)
(tan(x) − sin(x) sin(y)) dx + cos(x) cos(y) dy = 0

Determine whether the equation is exact. If it is exact, FIND
THE SOLUTION. If not write NOT EXACT.
A) (3x + 7) + (3y −
3)y' = 0
B) (7x2 − 2xy +
8) + (2y2 −
x2 + 7)y' = 0
C) (ex sin
y + 2y) − (2x
− ex sin
y)y' = 0
D) (y/x + 10x) + (lnx - 7) y' = 0 x>0

1- Find the solution of the following equations. For each
equation, 2- determine the type of the category that the equation
belongs to.
1. y/x cos y/x dx − ( x/y sin y/x + cos y/x ) dy = 0
2. x(1 − y^2 )dx + y(8 − x^2 )dy = 0
3. (x^2 − x + y^2 )dx − (e^y − 2xy)dy = 0
4. 2x sin 3ydx + 3x^2 cos 3ydy = 0
5. (x ln x −...

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=

The nonhomogeneous equation t2 y′′−2 y=19
t2−1, t>0, has homogeneous solutions
y1(t)=t2, y2(t)=t−1. Find the particular
solution to the nonhomogeneous equation that does not involve any
terms from the homogeneous solution.
Enter an exact answer.
Enclose arguments of functions in parentheses. For example,
sin(2x).
y(t)=

Transform the given system into a single equation of
second-order x′1 =−8x1+9x2 x′2 =−9x1−8x2. Then find x1 and x2 that
also satisfy the initial conditions x1(0) =7 x2(0) =3. Enter the
exact answers. Enclose arguments of functions in parentheses. For
example, sin(2x).

Determine if the ODE is an “exact equation.” If it is, find an
implicit
solution, or an explicit solution if you can. If you can say
anything about the solution
interval, do.
(x + y) 2 + (2xy + x 2 − 1)dy dx = 0

Q3. Determine whether the equation (y2cosx -
3x2y - 2x)dx + (2ysinx - x3 + lny)dy = 0
subject to initial condition y(0) = e is exact. If it is exact find
the implicit form of the solution of the IVP.

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