Question

t^2y''=(y')^2 assume y(1)=2, y'(1)=1 solve this second differential equation please

Answer 1

lalaly is typing a reply… :D

Answer 2

here y is absent
so u let y'=u
y''=du/dt

substitute in the question
\[t^2 \frac{du}{dt}=u^2\]now its a sepreble differential eqn\[\frac{du}{u^2}=\frac{dt}{t^2}\]\[-\frac{1}{u}=-\frac{1}{t}+C\]\[u=\frac{-t}{Ct-1}\]but u=y'\[ y'=\frac{-t}{Ct-1}\]now integrate

Answer 3

thanks so much