Question

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

Answer #1

1) Solve the given differential equation by finding, as in
Example 4 of Section 2.4, an appropriate integrating factor.
(14 − 20y +
e−5x)
dx − 4 dy = 0
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

For the below ordinary differential equation with initial
conditions, state the order and determine if the equation is linear
or nonlinear. Then find the solution of the ordinary differential
equation, and apply the initial conditions. Verify your solution.
x^2/(y^2-1) dy/dx=(3x^3)/y, y(0)=2

Solve the 1st order initial value problem:
1+(x/y+cosy)dy/dx=0, y(pi/2)=0

solve by the integrating facote method the following initial
value problem
dy/dx=y+x, y(0)=0

Consider the differential equation y′′+ 9y′= 0.(
a) Let u=y′=dy/dt. Rewrite the differential equation as a
first-order differential equation in terms of the variables u.
Solve the first-order differential equation for u (using either
separation of variables or an integrating factor) and integrate u
to find y.
(b) Write out the auxiliary equation for the differential
equation and use the methods of Section 4.2/4.3 to find the general
solution.
(c) Find the solution to the initial value problem y′′+ 9y′=...

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

For the below ordinary differential equation, state the order
and determine if the equation is linear or nonlinear. Then find the
general solution of the ordinary differential equation. Verify your
solution.
x dy/dx+y=xsin(x)
Please no handwriting unless I can read it.

Solve the initial-value problem for linear differential
equation
y'' + 4y' + 8y = sinx; y(0) = 1,
y'(0) = 0

solve for y:
1. dy/dx= xe^y separable
2. x(dy/dx)+3y=x^2 when y(5)=0 1st order linear

Solve the following equation using integrating factor.
y dx + (2x − ye^y) dy = 0

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