Question

The solution of the differential equation $\frac{d y}{d x}=(x+y)^{2}$ is

• A. $\tan ^{-1}(x+y)=x+c$
• B. $\cot ^{-1}(x+y)=c$
• C. $\tan ^{-1}(x+y)=0$
• D. $\cot ^{-1}(x+y)=x+c$

Answer 1

Answer: (A)

$x+y=z \Rightarrow \frac{d z}{d x}=1+z^{2}$
$\int \frac{1}{1+z^{2}} d z=\int 1 d x$
$\operatorname{Tan}^{-1}(x+y)=x+c$