Question

1. Find the general solution of the first order linear differential equation: 2*x*dy/dx -y-3/sqrt(x)=0. sqrt() = square root of ().

2. Are there any transient terms in the general solution? Justify your answer.

Answer #1

Find the general solution of the given differential equation
(x+!) dy/dx + (x+2)y = 2xe^-x
y = ______
Determine whether there are any transient terms in the general
solution.

(61). (Bernoulli’s Equation): Find the general solution of the
following first-order differential equations:(a) x(dy/dx)+y=
y^2+ln(x) (b) (1/y^2)(dy/dx)+(1/xy)=1

find the solution of the first order differential equation
(e^x+y + ye^y)dx +(xe^y - 1)dy =0 with initial value y(0)= -1

dy/dx = 2 sqrt(y/x) + y/x (x<0)
Find general solution of the given ODE

3. Find the general solution to the differential equation:
(x^2 + 1/( x + y) + y cos(xy)) dx + (y ^2 + 1 / (x + y) + x
cos(xy)) dy = 0

Find the general solution to the first-order linear differential
equation.
y' = -y(6-y)

3. Consider the differential equation: x dy/dx = y^2 − y
(a) Find all solutions to the differential equation.
(b) Find the solution that contains the point (−1,1)
(c) Find the solution that contains the point (−2,0)
(d) Find the solution that contains the point (1/2,1/2)
(e) Find the solution that contains the point (2,1/4)

find the general solution of the given differential equation.
Give the largest interval I over which the general solution is
defined. Determine whether there are any transient terms in the
general solution dy/dx +y = e3x

Consider the differential equation
x2 dy + y ( x + y) dx = 0 with the initial condition
y(1) = 1.
(2a) Determine the type of the differential equation. Explain
why?
(2b) Find the particular solution of the initial value problem.

The differential equation given as dy / dx = y(x^3) -
1.4y, y (0) = 1 is calculated by taking the current h = 0.2 at the
point x = 0.6 and calculated by the Runge-Kutta method from the 4th
degree, find the relative error.
analytical solution: y(x)=e^(0.25(x^4)-1.4x)

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