>
Exams
>
Mathematics
>
Differential equations
>
the general solution of the differential equation
Question:
The general solution of the differential equation
\((x^2y^2+y)dx-(x-2x^3y)dy=0\)
is
KEAM - 2022
KEAM
Updated On:
May 31, 2024
\(x^2y^2-\frac{y}{x}=C\)
\(x^3y+\frac{x}{y}=C\)
\(xy^2+\frac{y}{x}=C\)
\(xy^2-\frac{y}{x}=C\)
\(x^2y+\frac{y}{x}=C\)
Hide Solution
Verified By Collegedunia
The Correct Option is
D
Solution and Explanation
The correct option is (D) :
\(xy^2-\frac{y}{x}=C\)
Download Solution in PDF
Was this answer helpful?
0
0
Top Questions on Differential equations
If \[\frac{dx}{dy} = \frac{1 + x - y^2}{y}, \quad x(1) = 1,\]then $5x(2)$ is equal to:
JEE Main - 2024
Mathematics
Differential equations
View Solution
Let $\alpha$ be a non-zero real number. Suppose $f : \mathbb{R} \to \mathbb{R}$ is a differentiable function such that $f(0) = 2$ and \[\lim_{x \to \infty} f(x) = 1.\]If $f'(x) = \alpha f(x) + 3$, for all $x \in \mathbb{R}$, then $f(-\log 2)$ is equal to ________ .
JEE Main - 2024
Mathematics
Differential equations
View Solution
Let
\(f(x) = |2x^2 + 5|x - 3|, x \in \mathbb{R}\)
. If
\(m\)
and
\(n\)
denote the number of points were
\(f\)
is not continuous and not differentiable respectively, then
\(m + n\)
is equal to:
JEE Main - 2024
Mathematics
Differential equations
View Solution
Let \( y = y(x) \) be the solution of the differential equation \[\left( 1 + x^2 \right) \frac{dy}{dx} + y = e^{\tan^{-1}x}, \, y(1) = 0.\]Then \( y(0) \) is:
JEE Main - 2024
Mathematics
Differential equations
View Solution
Let \( y = y(x) \) be the solution of the differential equation \[\left( 2x \log_e x \right) \frac{dy}{dx} + 2y = \frac{3}{x} \log_e x, \, x>0 \, \text{and} \, y(e^{-1}) = 0.\] Then, \( y(e) \) is equal to:
JEE Main - 2024
Mathematics
Differential equations
View Solution
View More Questions
Questions Asked in KEAM exam
A Spherical ball is subjected to a pressure of 100 atmosphere. If the bulk modulus of the ball is 10
11
N/m
2
,then change in the volume is:
KEAM - 2023
mechanical properties of solids
View Solution
Two identical solid spheres,each of radius 10cm,are kept in contact. If the mass of inertia of this system about the tangent passing through the point of contact is 0. Then mass of each sphere is:
KEAM - 2023
System of Particles & Rotational Motion
View Solution
The value of a(≠0) for which the equation
\(\frac{1}{2}(x-2)^2+1=\sin(\frac{a}{x})\)
holds is/are
KEAM - 2023
Trigonometric Functions
View Solution
\(∫xlog(1+x^2)dx=\)
?
KEAM - 2023
Integration by Parts
View Solution
A uniform thin rod of mass 3kg has a length of 1m. If a point mass of 1kg is attached to it at a distance of 40cm from its center,the center of mass shifts by a distance of:
KEAM - 2023
System of Particles & Rotational Motion
View Solution
View More Questions