Solve the following differential equations: $($a$)$ dp dt $=$ t $2$ p $5$p $+$ t $25.[5]($b$)$ cos$($x$)$ sec$2($y$)$ dy dx $=$ csc$2($y$)$ sec$($x$).[5]($c$)($e y $5)$y $=2+$ cos x$.$