Question:
The solution of the differential equation
\[
\frac{dy}{dx}=1+y^2
\]
is
The solution of the differential equation
\[
\frac{dy}{dx}=1+y^2
\]
is
Show Hint
Remember \(\int\frac{dy}{1+y^2}=\tan^{-1}y\).
Updated On: May 7, 2026
- \(y=\tan x+c\)
- \(y=\tan(x+c)\)
- \(y=\tan x\)
- \(y=-\tan(x+c)\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Given: \[ \frac{dy}{dx}=1+y^2 \]
Step 2: Separate variables: \[ \frac{dy}{1+y^2}=dx \]
Step 3: Integrate both sides: \[ \int\frac{dy}{1+y^2}=\int dx \] \[ \tan^{-1}y=x+c \]
Step 4: Taking tangent both sides: \[ y=\tan(x+c) \] \[ \boxed{y=\tan(x+c)} \]
Was this answer helpful?
0
0
Top AP ECET Agricultural Engg Mathematics Questions
- \[ \int_{-a}^{a}|x|\,dx= \]
- In the matrix $A=\begin{bmatrix}1& 2& 3 \\ 4& 5 & 6 \\ 7& 4 & 9\end{bmatrix}$, the minor $M_{23}$ of the $a_{23}$ is
- If $\begin{vmatrix}2x& 5 \\ 8 & x\end{vmatrix}=\begin{vmatrix}6 &-2 \\ 7& 3\end{vmatrix}$ then the value of $x$ is
- If $A$ is a square matrix of order 3 and $|A|=5$, then the value of $|2A^{T}|$ is
- Which of the following systems has non-trivial solution?
View More Questions
Top AP ECET Agricultural Engg Differential equations Questions
- The solution of the differential equation $x\frac{dy}{dx} + y = 0$ passing through the point (1,1) is $y =$
- Degree of the differential equation $y = x\frac{dy}{dx} + a\sqrt{1 + (\frac{dy}{dx})^2}$ is
- The order of the differential equation of all circles passing through the origin and having their centers on the x-axis is
- If $a$ and $b$ are arbitrary constants, then the differential equation representing the family of curves $y = a \sin(x + b)$ is
- The differential equation is $\frac{dy}{dx} + \frac{y}{x} = 0$ and $y(1) = 2$. Then the value of $y(3) =$
View More Questions
Top AP ECET Agricultural Engg Questions
- \[ \int_{-a}^{a}|x|\,dx= \]
- Rubber roll Sheller can shell up to percentage of paddy fed to it:
- The equipment used for separation of broken rice from head rice is:
- The efficiency of a cyclone separator increases by:
- Char-coal is made through process:
View More Questions