[Math] Solving the differential equation $dr=(r\cos\theta +r\sin\theta)d\theta$

Question

$dr=(r\cos\theta +r\sin\theta)d\theta$ In my book this is under separation of variables then i tried to factor out r and divide both sides then integrate both sides but where can i find my $C_1$? I just got $\ln(r)=\sin\theta-\cos\theta$

Answer 1

When taking an indefinite integral you add a constant of integration

$$\int\frac{1}{r}dr=\int(cos(\theta)+sin(\theta))d\theta$$

$$ln|r|=sin(\theta)-cos(\theta)+C$$