Bernoulli’s Equation - Practice Questions & MCQ

When DE is not in the linear form, it can sometimes be converted into a linear form with the help of proper substitution.

An equation of the form

$
\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{P}(\mathrm{x}) \cdot \mathrm{y}=\mathrm{Q}(\mathrm{x}) \cdot \mathrm{y}^{\mathrm{n}}
$

Where $\mathrm{P}(\mathrm{x})$ and $\mathrm{Q}(\mathrm{x})$ are a function of x only, is known as Bernoulli's equation.
(If we put $\mathrm{n}=0$, then the equation is in linear form.)
To reduce Eq (i) into linear form, divide both sides by $\mathrm{y}^{\mathrm{n}}$,
$
\begin{gathered}
\frac{1}{y^n} \cdot \frac{d y}{d x}+\frac{P(x)}{y^{n-1}}=Q(x) \\
\text { or } \quad y^{-n} \cdot \frac{d y}{d x}+y^{1-n} \cdot P(x)=Q(x)
\end{gathered}
$

Putting $y^{1-n}=t$, converts this equation into a linear equation in $t$, which can then be solved