Maple da differensial tenglamalar

> infolevel[dsolve] := 4;



>eq4:=x^2*y(x)*diff(y(x),x,x)-(y(x)-x*diff(y(x),x))^2=0;



>dsolve(eq4);

‘Methods for second order ODEs:’

‘   *** Sublevel 2 ***’
‘   Methods for second order ODEs:’
‘   --- Trying classification methods ---’
‘   trying 2nd order Liouville’
‘   trying 2nd order, 2 integrating factors of the form mu(x,y)’
‘   -> Linearization is possible. Trying to determine two integrating fa\
ctors as solutions to a 2nd order linear ODE’
‘   -> Tackling the linear ODE "as given":’
‘      trying a quadrature’
‘      checking if the LODE has constant coefficients’
‘      checking if the LODE is of Euler type’
‘      <- LODE of Euler type successful’
‘   <- successful solving of the linear ODE "as given"‘

‘   <- 2nd order, 2 integrating factors of the form mu(x,y) successful’

Displeyga chiqarilgan ma’lumotlardan ko‘rinadiki, tenglama-ni yechishda integrallovchi ko‘paytuvchi usuli qo‘l kelgan; ikkita integrallovchi ko‘paytuvchi topilgan va berilgan tenglama yechilib, uning

yechimlari hosil qilingan. Bundan umumiy yechim formula bilan berilishi kelib chiqadi.

Ushbu tenglamaning yechimini oshkormas ko‘rinishda izlash qulay.