What's the dimension of the solution space of $x^2y'' − 4xy' + 6y = 0$ on $(−1, 1)$?
The answer is $3$.
How is this possible? Isn't the basis $\{x^2 , x^3\}$?
2026-03-29 21:02:43.1774818163
The dimension of the solution space of $x^2y'' − 4xy' + 6y = 0$ on $(−1, 1)$ is?
199 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ORDINARY-DIFFERENTIAL-EQUATIONS
- The Runge-Kutta method for a system of equations
- Analytical solution of a nonlinear ordinary differential equation
- Stability of system of ordinary nonlinear differential equations
- Maximal interval of existence of the IVP
- Power series solution of $y''+e^xy' - y=0$
- Change of variables in a differential equation
- Dimension of solution space of homogeneous differential equation, proof
- Solve the initial value problem $x^2y'+y(x-y)=0$
- Stability of system of parameters $\kappa, \lambda$ when there is a zero eigenvalue
- Derive an equation with Faraday's law
Related Questions in DIFFERENTIAL
- In a directional slope field, how can a straight line be a solution to a differential equation?
- The Equation of Motion of a Snowball
- Supremum of the operator norm of Jacobian matrix
- Directional continuous derivative on vectors of a base implies differentiability in $\mathbb{R}^n$
- Need explanation for intuition behind rewriting $dy$ in terms of $dx$
- Does the double integrative of d^{2}x make sense from a mathematical point of view?
- Functional with 4th grade characteristic equation
- need to equate MATLAB and MATHEMATICA solutions
- Formula for Curvature
- Showing that $\Psi(f) = \int^{b}_{a}\phi(f(x))dx$ is differentiable.
Related Questions in CHANGE-OF-BASIS
- Alternate basis for a subspace of $\mathcal P_3(\mathbb R)$?
- I don't understand this $\left(\left[T\right]^B_C\right)^{-1}=\left[T^{-1}\right]^C_B$
- What is meant by input and output bases?
- Change of Basis of Matrix: Two points of view
- Change of Basis (Transformation Matrix)
- Diagonalization and change of basis
- Change of Basis Matrix. Doubt about notation.
- Why does the method of getting a transition matrix seems reversed to me?
- Finding bases to GF($2^m$) over GF($2$)
- Block diagonalizing a Hermitian matrix
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
What about this solution? $$ y(x) = \begin{cases} x^3, & x \ge 0 \\ -x^3, & x < 0 \end{cases} $$