[tex]\mathrm dy+k(y-70)\,\mathrm dx=0[/tex]
Separating variables gives
[tex]\dfrac{\mathrm dy}{y-70}=-k\,\mathrm dx[/tex]
Integrating both sides gives
[tex]\displaystyle\int\frac{\mathrm dy}{y-70}=-k\int\mathrm dx[/tex]
[tex]\ln|y-70|+C_1=-kx+C_2[/tex]
[tex]\ln|y-70|=-kx+C[/tex]
Solving for [tex]y[/tex] gives
[tex]e^{\ln|y-70|}=e^{-kx+C}[/tex]
[tex]y-70=e^{-kx}e^C[/tex]
[tex]y=Ce^{-kx}+70[/tex]
As [tex]y(1)=140[/tex], you get
[tex]140=Ce^{-k}+70[/tex]
[tex]70=Ce^{-k}[/tex]
[tex]C=70e^k[/tex]
so the particular solution to this ODE is
[tex]y=70e^ke^{-kx}+70[/tex]
[tex]y=70e^{k(1-x)}+70[/tex]
Unless you have any more information, you're done.
