Question

1. Sketch the direction field for the following differential equation dy dx = y − x. You may use maple and attach your graph. Also sketch the solution curves with initial conditions y(0) = −1 and y(0) = 1.

Answer #1

Use
a slope field plotter to plot the slope field for the differential
equation
dy/dx=sqrt(x-y)
and plot the solution curve for the initial condition
y(2)=2

Solve the Homogeneous differential equation
(7 y^2 + 1 xy)dx - 1 x^2 dy = 0
(a) A one-parameter family of solution of the equation is y(x)
=
(b) The particular solution of the equation subject to the
initial condition y(1) =1/7.

(x-y)dx + (y+x)dy =0 Solve the differential equation

(* Problem 3 *)
(* Consider differential equations of the form a(x) + b(x)dy
/dx=0 *) \
(* Use mathematica to determin if they are in Exact form or not.
If they are, use CountourPlot to graph the different solution
curves 3.a 3x^2+y + (x+3y^2)dy /dx=0 3.b cos(x) + sin(x) dy /dx=0
3.c y e^xy+ x e^xydy/dx=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 differential equation
y-x(dy/dx)=3-2x2(dy/dx)

(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

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)

exact differential equation, (2xy+x)dx+(x^2+y)dy=0

Use the method for solving homogeneous equations to solve the
following differential equation.
(9x^2-y^2)dx+(xy-x^3y^-1)dy=0
solution is F(x,y)=C, Where C= ?

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