Write the equation in the form y$=$f$($y$/$x$)$ then use the substitution y$=$xu to find an implicit general solution. Then solve the initial value problem.

y$=(5$y$+4$x$)/$x$,$y$(1)=5$

The resulting differential equation in x and u can be written as xu$=$

which is separable.

Separating variables we arrive at

du$=$dxx

Integrating both sides and simplifying, the solution can be written in the form u$+1=$Cf$($x$)$ where C is an arbitrary constant and f$($x$)=$

Transforming back into the variables x ans y and using the initial condition to find C we find the explicit solution of the initial value problem is

y$=$