Question:
Given that y(x) is a solution of the deferential equation
\(x^2y''+xy'-4y-x^2\)
on the interval (0,∞) such that the \(lim_{x→0^+}\) y(x) exists and y(1)=1. the value y'(1) is qual to____.(Rounded off to two decimal places).
Given that y(x) is a solution of the deferential equation
\(x^2y''+xy'-4y-x^2\)
on the interval (0,∞) such that the \(lim_{x→0^+}\) y(x) exists and y(1)=1. the value y'(1) is qual to____.(Rounded off to two decimal places).
\(x^2y''+xy'-4y-x^2\)
on the interval (0,∞) such that the \(lim_{x→0^+}\) y(x) exists and y(1)=1. the value y'(1) is qual to____.(Rounded off to two decimal places).
Updated On: Oct 1, 2024
Hide Solution
Verified By Collegedunia
Correct Answer: 2.24 - 2.26
Solution and Explanation
The correct answer is: 2.24 to 2.26 (approx)
Was this answer helpful?
0
0
Top Questions on Differential Equations
- The integrating factor of the differential equation \[ (y \log_e y) \frac{dx}{dy} + x = 2 \log_e y \] is:
- CUET (UG) - 2024
- Mathematics
- Differential Equations
- If the solution of the differential equation \[ \frac{dy}{dx} = \frac{ax + 3}{2y + 5} \] represents a circle, then $a$ is equal to:
- CUET (UG) - 2024
- Mathematics
- Differential Equations
- Let \( y = y(x) \) be the solution of the differential equation\[\frac{dy}{dx} + \frac{2x}{\left( 1 + x^2 \right)^2} y = x e^{\frac{1}{1+x^2}}, \quad y(0) = 0. \] Then the area enclosed by the curve \[ f(x) = y(x) e^{\frac{1}{1+x^2}} \]and the line \( y - x = 4 \) is _______.
- JEE Main - 2024
- Mathematics
- Differential Equations
- The differential equation of the family of circles passing the origin and having center at the line y = x is:
- JEE Main - 2024
- Mathematics
- Differential Equations
- If \( y = y(x) \) is the solution of the differential equation \(\frac{dy}{dx} + 2y = \sin(2x), \quad y(0) = \frac{3}{4},\)then \(y\left(\frac{\pi}{8}\right)\) is equal to:
- JEE Main - 2024
- Mathematics
- Differential Equations
View More Questions
Questions Asked in IIT JAM MA exam
- For n ≥ 3, let a regular n-sided polygon Pn be circumscribed by a circle of radius Rn and let rn be the radius of the circle inscribed in Pn. Then
\(\lim\limits_{n \rightarrow \infin}(\frac{R_n}{r_n})^{n^2}\)
equals- IIT JAM MA - 2024
- Sequences and Series
- Consider the function f: ℝ → ℝ given by f(x) = x3 - 4x2 + 4x - 6.
For c ∈ ℝ, let
\(S(c)=\left\{x \in \R : f(x)=c\right\}\)
and |S(c)| denote the number of elements in S(c). Then, the value of
|S(-7)| + |S(-5)| + |S(3)|
equals _________- IIT JAM MA - 2024
- Functions of One Real Variable
- For a > b > 0, consider
\(D=\left\{(x,y,z) \in \R^3 :x^2+y^2+z^2 \le a^2\ \text{and } x^2+y^2 \ge b^2\right\}.\)
Then, the surface area of the boundary of the solid D is- IIT JAM MA - 2024
- Functions of Two or Three Real Variables
- Consider the 4 × 4 matrix
\(M = \begin{pmatrix} 0 & 1 & 2 & 3 \\ 1 & 0 & 1 & 2 \\ 2 & 1 & 0 & 1 \\ 3 & 2 & 1 & 0 \end{pmatrix}\)
If ai,j denotes the (i, j)th entry of M-1 , then a4,1 equals __________ (rounded off to two decimal places).- IIT JAM MA - 2024
- Matrices
- Let
S = {f: ℝ → ℝ ∶ f is a polynomial and f(f(x)) = (f(x))2024 for x ∈ ℝ}.
Then, the number of elements in S is _____________- IIT JAM MA - 2024
- Functions of One Real Variable
View More Questions