An equation of motion when a particle moves in a resting medium is given by

$$\frac{\mathrm{d}v}{\mathrm{d}t}}=-(kv+bt)$$

where k and b are constants. Given that v=u when t=0, show that

$$v(t)={\textstyle \frac{b}{{k}^{2}}}-{\textstyle \frac{b}{k}}t+(u-{\textstyle \frac{b}{{k}^{2}}}){e}^{-kt}$$

$$\frac{\mathrm{d}v}{\mathrm{d}t}}=-(kv+bt)$$

where k and b are constants. Given that v=u when t=0, show that

$$v(t)={\textstyle \frac{b}{{k}^{2}}}-{\textstyle \frac{b}{k}}t+(u-{\textstyle \frac{b}{{k}^{2}}}){e}^{-kt}$$