How do I solve the differential equation $y^2= 2px+ p^2 $, $\ $ $p$ $\ $ being $\frac{dy}{dx}$? I came up with this equation accidentally while trying to copy an exercise from the book. The actual problem is fine, but this equation is troubling me for a while. I tried reducing it to Clairaut's form to no avail. I tried solving for $y$ or $x$, but failed. Kindly help me out.
2026-05-14 14:23:11.1778768591
Solving a non-linear differential equation of second degree
72 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated 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 DERIVATIVES
- Derivative of $ \sqrt x + sinx $
- Second directional derivative of a scaler in polar coordinate
- A problem on mathematical analysis.
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- Does there exist any relationship between non-constant $N$-Exhaustible function and differentiability?
- Holding intermediate variables constant in partial derivative chain rule
- How would I simplify this fraction easily?
- Why is the derivative of a vector in polar form the cross product?
- Proving smoothness for a sequence of functions.
- Gradient and Hessian of quadratic form
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
geometry
circles
algebraic-number-theory
functions
real-analysis
elementary-set-theory
proof-verification
proof-writing
number-theory
elementary-number-theory
puzzle
game-theory
calculus
multivariable-calculus
partial-derivative
complex-analysis
logic
set-theory
second-order-logic
homotopy-theory
winding-number
ordinary-differential-equations
numerical-methods
derivatives
integration
definite-integrals
probability
limits
sequences-and-series
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?