Question

solve (dy/dx)^2-x dy/dx+y=0

Answer 1

Maybe You could use the equation tool to express yourself more clearly :)

Answer 2

@BSwan help him

Answer 3

y''-xy'+y=0
i hate partial equations xD

Answer 4

power series solution o_o

Answer 5

nope

Answer 6

i may be correct or not.
i denote \[\frac{ dy }{ dx }=y \prime,~and~\frac{ d^2y }{ dx^2 }=y \prime \prime \]
\[\left( y' \right)^2-x y'+y=0\]
differentiate again
\[2 y'y \prime \prime -xy \prime \prime -y'+y'=0,\]
\[\left( 2y \prime-x \right)y \prime \prime=0\]
either \[y \prime \prime=0,\frac{ d^2y }{ dx^2 }=0,\]
integrating
\[\frac{ dy }{ dx }=c _{1}\]
again integrating
\[y=c _{1}x+c _{2}\]
\[2y \prime=x,\frac{ dy }{ dx }=\frac{ 1 }{ 2 }x\]
separate the variables and integrating
\[y=\frac{ 1 }{ 4 }x^2+c _{3}\]

Answer 7

hats off for u

Answer 8

someone posted this problem yesterday
but i did not see anywhere.
so i posted and wrote the solution which came in my mind.