Question

The solution of the differential equation $\frac{dy}{dx}=5+5x+10y+10xy$ is

• A. $\log (5+10y)=x+\frac{x^2}{2}+c$
• B. $\frac{1}{10}\log (5+10y)=x+\frac{x^2}{2}+c$
• C. $\frac{1}{5}\log (5+10y)=x+\frac{x^2}{2}+c$
• D. $\frac{1}{10}\log (5-10y)=x+\frac{x^2}{2}+c$

Answer 1

Answer: (B)

$[\because \frac{dy}{dx}=5\left(1+x\right)+10y\left(1+x\right)$
$=\left(1+x\right)\left(5+10y\right)$
$\therefore \frac{10dy}{10\left(5+10y\right)}=\left(1+x\right)dx$
$\Rightarrow \frac{1}{10}log\left(5+10y\right)=x+\frac{x^2}{2}+c$