Isistatome sia funkcija i pradine nehomogenine lygti ir randame antraja pilnojo sprendinio dali:
C'(x)/sqrt(1-x^2)=1/(1-x^2) => C'(x)=1/sqrt(1-x^2) =>
C(x)=arcsin(x)
Pilnas lygties sprendinys:
y(x)=const/sqrt(1-x^2) + arcsin(x)/sqrt(1-x^2), kur const yra bet koks realusis skaicius
y'(x)=xy/(1-x^2) => y(x)=C(x)/sqrt(1-x^2)
Isistatome sia funkcija i pradine nehomogenine lygti ir randame antraja pilnojo sprendinio dali:
C'(x)/sqrt(1-x^2)=1/(1-x^2) => C'(x)=1/sqrt(1-x^2) =>
C(x)=arcsin(x)
Pilnas lygties sprendinys:
y(x)=const/sqrt(1-x^2) + arcsin(x)/sqrt(1-x^2), kur const yra bet koks realusis skaicius