Question

Previous Problem Problem List Next Problem (1 point) The equation $4xy' = 4x^2 + 4x^2 + y^2$ can be written in the form $y' = f(y/x)$, i.e., it is homogeneous, so we can use the substitution $u = y/x$ to obtain a separable equation with dependent variable Introducing this substitution and using the fact that $y' = xu' + u$ we can write (*) as $xu' + u = f(u)$ where $f(u) = $ Separating variables we can write the equation in the form $g(u) du = \frac{dx}{x}$ where $g(x) = $ An implicit general solution with dependent variable $u$ can be written in the form $\ln(|x|) = $ $C. Transforming $u = y/x$ back into the variables $x$ and $y$ and using the initial condition $y(1) = 2$ we find $C = $ Finally solve for $y$ to obtain the explicit solution of the initial value problem $y = $

          Previous Problem Problem List Next Problem
(1 point)
The equation
$4xy' = 4x^2 + 4x^2 + y^2$
can be written in the form $y' = f(y/x)$, i.e., it is homogeneous, so we can use the substitution $u = y/x$ to obtain a separable equation with dependent variable
Introducing this substitution and using the fact that $y' = xu' + u$ we can write (*) as
$xu' + u = f(u)$ where $f(u) = $
Separating variables we can write the equation in the form
$g(u) du = \frac{dx}{x}$
where $g(x) = $
An implicit general solution with dependent variable $u$ can be written in the form
$\ln(|x|) = $
$C.
Transforming $u = y/x$ back into the variables $x$ and $y$ and using the initial condition $y(1) = 2$ we find
$C = $
Finally solve for $y$ to obtain the explicit solution of the initial value problem
$y = $

Previous Problem Problem List Next Problem
(1 point)
The equation
4xy' = 4x^2 + 4x^2 + y^2
can be written in the form y' = f(y/x), i.e., it is homogeneous, so we can use the substitution u = y/x to obtain a separable equation with dependent variable
Introducing this substitution and using the fact that y' = xu' + u we can write (*) as
xu' + u = f(u) where f(u) =
Separating variables we can write the equation in the form
g(u) du = (dx)/(x)
where g(x) =
An implicit general solution with dependent variable u can be written in the form
ln(|x|) =
C.
Transformingu = y/xback into the variablesxandyand using the initial conditiony(1) = 2we findC = Finally solve foryto obtain the explicit solution of the initial value problemy =

Added by Jimmy W.

Question

Please give Ace some feedback