# Q. 2# (x+1)frac{dy}{dx}=x(y^{2}+1)

Jason Farmer 2021-02-08 Answered
Q. 2# $\left(x+1\right)\frac{dy}{dx}=x\left({y}^{2}+1\right)$
You can still ask an expert for help

Expert Community at Your Service

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Available 24/7
• Math expert for every subject
• Pay only if we can solve it

## Expert Answer

unessodopunsep
Answered 2021-02-09 Author has 105 answers
Here the Differential equations is given by
$\left(x+1\right)\frac{dy}{dx}=x\left({y}^{2}+1\right)$
$\to \frac{dy}{{y}^{2}+1}=\frac{xdx}{x+1}$
$\to \int \frac{dy}{{y}^{2}+1}=\int \frac{xdx}{x+1}$
$\to {\mathrm{tan}}^{-1}\left(y\right)=\int \frac{x+1-1dx}{\left(x+1\right)+c}$
$\to {\mathrm{tan}}^{-1}\left(y\right)=\int \frac{\left(x+1-1\right)dx\right)}{x+1+c}$
$\to {\mathrm{tan}}^{-1}\left(y\right)=\int dx-\int \frac{dx}{\left(x+1\right)+c}$
$\to {\mathrm{tan}}^{-1}\left(y\right)=x-\mathrm{ln}\mid x+1\mid +c$
$\to y=tan\left(x-\mathrm{ln}\mid x+1\mid +c\right),$
where cc is a arbitrary constant.
###### Not exactly what you’re looking for?

Expert Community at Your Service

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Available 24/7
• Math expert for every subject
• Pay only if we can solve it