Question

The solution of $\frac{dy}{dx}=\sqrt{1+x+y+xy}$ is:

• A. $\sqrt{1+y}=\sqrt{1+x}+c$
• B. $\frac{2}{3}\sqrt{1+y}={(1+x)}^{\frac{1}{2}}+c$
• C. $3\sqrt{1+y}={(1+x)}^{\frac{3}{2}}+c]$
• D. $\sqrt{1+x}=\sqrt{1+y}=c$

Answer 1

Answer: (C)

$3\sqrt{1+y}={(1+x)}^{\frac{3}{2}}+c]$

$\Rightarrow \frac{dy}{dx}=\sqrt{1+xy+x+y}=\sqrt{(1+x)(1+y)}$

$\Rightarrow \int \frac{dy}{\sqrt{y+1}}=\int \sqrt{x+1}dx+c$

$\Rightarrow 2\sqrt{y+1}=\frac{2}{3}(x+1{)}^{3/2}+c$

$\Rightarrow 3\sqrt{y+1}=(x+1{)}^{3/2}+c$