A special class of first$-$order linear equations have the form $a(t)y^{\text{'}}(t)a^{\text{'}}(t)y(t)=f(t),$ where a and $f$ are given functions of $t.$ Notice that the left side of this equation can be written as the derivative of a product, so the equation has the form $\frac{d^{\text{'}}}{dt}(a(t)y(t))=a(t)y^{\text{'}}(t)a^{\text{'}}(t)y(t)=f(t).$ Therefore, the equation can be solved by integrating both sides with respect to $t.$ Use this idea to solve the following.

$t{y}^{\text{'}}(0)y=52t,y(1)=7$

$y(t)=$ where $t>0$