Question

solve the following ordinary differential eq.
x*(d^2u/dx^2) = 5*(du/dx)
Hint: substitute v= du/dx

Answer 1

help!

Answer 2

make the substitution, notice 2nd derivative of u equals 1st derivative of v
\[x*\frac{dv}{dx} = 5v\]
then separate variables
\[\frac{dv}{v} = \frac{5}{x} dx\]
then integrate both sides to solve for v

Answer 3

once you have v, integrate again to get u

note: you will have 2 constants of integration in answer