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)

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