Question

dy/dx = x^4/y^2

a) use eulers method to approximate the solution at x =1.6
starting at the initial condition of y(1)=1 and a step size of
delta x=0.2

b) solve this differential equation exactly using separation
if variables and the inital condition y(1)=1

c) what is the exact vwlue of y(1.6) for the solution found in
part b

Answer #1

dy/dx = x^4/y^2
initial condition y(1)= 1
a) use eulers method to approximate the solution at x=1.6 and
a step size od delta x = 0.2
b) solve the differential equation exactly using seperation
variabled and the intial condtion y(1)=1.
c) what is the exact value of y(1.6) for your solution from
part b.

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

(a) State the interval on which the solution to the differential
equation (x^2-1)dy/dx + ln(x+1)y = 4e^x
with initial condition y(2) = 4 exists. Do not attempt to solve the
equation.
ODE
SHOW ALL STEPS PLEASE.

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.

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.

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)

Consider the following differential equation: dy/dx =
−(3xy+y^2)/x^2+xy
(a) Rewrite this equation into the form M(x, y)dx + N(x, y)dy =
0. Determine if this equation is exact;
(b) Multiply x on both sides of the equation, is the new
equation exact?
(c) Solve the equation based on Part (a) and Part (b).

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= ?

test if the equation ((x^4)(y^2) - y)dx + ((x^2)(y^4) - x)dy = 0 is
exact. If it is not exact, try to find an integrating factor. after
the equation is made exact, solve by looking for integrable
combinations

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

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