Question

Solve the following initial value problem,

dy/dx = 8cos(x) / (y^{2} + 4y + 4)

y(π/4) = 4

Answer #1

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 Initial Value Problem
(y2 cos(x) − 3x2y − 2x) dx + (2y sin(x) −
x3 + ln(y)) dy = 0, y(0) = e

1) Consider the following initial-value problem.
(x + y)2 dx + (2xy + x2 − 2) dy =
0, y(1) = 1
Let af/ax = (x + y)2 = x2 + 2xy +
y2.
Integrate each term of this partial derivative with respect to
x, letting h(y)
be an unknown function in y.
f(x, y) = + h(y)
Find the derivative of h(y).
h′(y) =
Solve the given initial-value problem.
2) Solve the given initial-value problem.
(6y + 2t − 3)
dt...

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 initial-value problem.
(x2 + 1)
dy
dx
+ 3x(y − 1) = 0,
y(0) = 4

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)

1) Solve the given differential equation by separation of
variables.
exy
dy/dx = e−y +
e−6x −
y
2) Solve the given differential
equation by separation of variables.
y ln(x) dx/dy = (y+1/x)^2
3) Find an explicit solution of the given initial-value
problem.
dx/dt = 7(x2 + 1), x( π/4)= 1

Solve the initial value problem
dy/dy-y/x=7xe^x y(1)=7e+3

Solve the given initial-value problem. The DE is a Bernoulli
equation.
x2 dy/dx-2xy=5y^4, y(1)=1/2

differential equations solve
(2xy+6x)dx+(x^2+4y^3)dy, y(0)=1

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