Question

1) Solve the given differential equation by finding, as in Example 4 of Section 2.4, an appropriate integrating factor.

(14 − 20* y* +

2) Solve the given initial-value problem.

x dy/ dx + y = 2x + 1, y(1) = 9

y(x) =

Give the largest interval *I* over which the solution is
defined. (Enter your answer using interval notation.)

I =

please show steps

Answer #1

Solve the given differential equation by finding, as in Example
4 of Section 2.4, an appropriate integrating factor.
(14 − 10y +
e−5x)
dx − 2 dy = 0

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

Solve the differential equation (5x^4 y^2+ 2xe^y - 2x cos (x^2)) dx
+ (2x^5y + x^2 e^y) dy = 0.

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 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 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

(a) Use an Integrating Factor to solve the ordinary differential
equation,
r dy/dr + 2y = 4 ln r,
subject to the initial condition, y(1) = 0. [5 marks]
(b) Solve the ordinary differential equation which is given in
part (a) by first making the substitution, r = e x , to transform
it into a differential equation for y in terms of x. [5 marks]

Solve the given differential equation by using an appropriate
substitution. The DE is of the form dy dx = f(Ax + By + C), which
is given in (5) of Section 2.5. dy/dx = (x + y + 7)^2

Solve the differential equation, (8 - 12y +
e-3x)dx - 4dy = 0, by finding an appropriate
integrating factor.

solve the given differential equation by using an
appropriate substitution. The DE is a Bernoulli equation. x * dy/dx
+ y = 1/y^2

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