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

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

Question
Differential equations
asked 2021-02-08
Q. 2# \((x+1)\frac{dy}{dx}=x(y^{2}+1)\)

Answers (1)

2021-02-09
Here the Differential equations is given by
\((x+1)\frac{dy}{dx}=x(y^{2}+1)\)
\(\rightarrow\frac{dy}{y^{2}+1}= \frac{xdx}{x+1}\)
\(\rightarrow\int\frac{dy}{y^{2}+1}=\int\frac{xdx}{x+1}\)
\(\rightarrow \tan^{−1}(y)=\int\frac{x+1−1dx}{(x+1)+c}\)
\(\rightarrow \tan^{−1}(y)=\int\frac{(x+1−1)dx)}{x+1+c}\)
\(\rightarrow \tan^{−1}(y)=\int dx−\int\frac{dx}{(x+1)+c}\)
\(\rightarrow \tan^{−1}(y)=x−\ln∣x+1∣+c\)
\(\rightarrow y=tan(x−\ln∣x+1∣+c),\)
where cc is a arbitrary constant.
0

Relevant Questions

asked 2021-03-22
Solve the equation:
\(\displaystyle{\left({x}+{1}\right)}{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={x}{\left({y}^{{2}}+{1}\right)}\)
asked 2021-05-10
Solve the equation:
\(\displaystyle{\left({a}-{x}\right)}{\left.{d}{y}\right.}+{\left({a}+{y}\right)}{\left.{d}{x}\right.}={0}\)
asked 2021-05-11
Calculating derivatives Find dy>dx for the following functions.
\(\displaystyle{y}={\frac{{{1}}}{{{2}+{\sin{{x}}}}}}\)
asked 2021-03-20
The graph of y = f(x) contains the point (0,2), \(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{-{x}}}{{{y}{e}^{{{x}^{{2}}}}}}}\), and f(x) is greater than 0 for all x, then f(x)=
A) \(\displaystyle{3}+{e}^{{-{x}^{{2}}}}\)
B) \(\displaystyle\sqrt{{{3}}}+{e}^{{-{x}}}\)
C) \(\displaystyle{1}+{e}^{{-{x}}}\)
D) \(\displaystyle\sqrt{{{3}+{e}^{{-{x}^{{2}}}}}}\)
E) \(\displaystyle\sqrt{{{3}+{e}^{{{x}^{{2}}}}}}\)
asked 2021-05-07
Find \(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}\) using the rules for finding derivatives.
\(\displaystyle{y}={\left({2}{x}^{{{2}}}-{6}\right)}{\left({8}{x}^{{{2}}}-{9}{x}+{9}\right)}\)
\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}=\)
asked 2020-10-26
Find the differential dy for the given values of x and dx. \(y=\frac{e^x}{10},x=0,dx=0.1\)
asked 2020-11-24
Q. 1# \((a−x)dy+(a+y)dx=0(a−x)dy+(a+y)dx=0\)
asked 2021-01-31
Q. 1# \(\displaystyle{\left({a}−{x}\right)}{\left.{d}{y}\right.}+{\left({a}+{y}\right)}{\left.{d}{x}\right.}={0}{\left({a}−{x}\right)}{\left.{d}{y}\right.}+{\left({a}+{y}\right)}{\left.{d}{x}\right.}={0}\)
asked 2021-04-06
\(\displaystyle{Q}={\int_{{4}}^{{9}}}{\frac{{{3}{x}+{12}}}{{{x}^{{2}}+{6}{x}+{9}}}}{\left.{d}{x}\right.}\)
Determine the numerical values of the coefficients, A and B, where \(\displaystyle{A}\leq{B}\).
\(\displaystyle{\frac{{{A}}}{{{d}{e}{n}{o}{m}{i}{a}{n}{a}\to{r}}}}+{\frac{{{B}}}{{{d}{e}{n}{o}{m}{i}{a}{n}\to{r}}}}\)
Need to find A and B.
asked 2021-06-05
Find \(\frac{dy}{dx}\) in xy = x+y
...