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I’m a student studying CSE at Jaypee University of Information Technology.

$y^{\prime \prime}+y y^{\prime}=t^{2}-1$; $y(0)=1$, $y^{\prime}(0)=-1$

$(1-t) y^{\prime \prime}+t y^{\prime}-2 y=\sin t$; $y(0)=1$, $y^{\prime}(0)=1$

$t^{2} \frac{d^{2} y}{d t^{2}}+2 t \frac{d y}{d t}-6 y=0$

$\frac{d^{2} w}{d t^{2}}+\frac{6}{t} \frac{d w}{d t}+\frac{4}{t^{2}} w=0$

$t^{2} y^{\prime \prime}(t)-3 t y^{\prime}(t)+4 y(t)=0$

$t^{2} y^{\prime \prime}(t)-3 t y^{\prime}(t)+6 y(t)=0$