Updated on March 16, 2024

In the world of mathematics and beyond, the term *equation* carries vast significance, but it's the adjectives paired with it that add depth and perspective. A **differential opens up discussions about change and rates, while an ****above equation** might hint at something exceeding standard expectations. The simplicity found in a **linear equation** contrasts with the comprehensive nature of a **general equation**, showing the breadth of mathematical inquiries. Moreover, a **characteristic equation** could reveal unique attributes essential to understanding complex systems, and a **second equation** might introduce a subsequent layer of complexity or clarification. Each adjective nuances our understanding and application of equations in fascinating ways. Discover more about how adjectives color our comprehension of equations below.

differential | The differential equation y' = y can be solved by separation of variables. |

above | The result of the above equation is 10. |

linear | The equation 2x + 5 = 11 is a linear equation |

general | The general equation of a circle is (x - h)^2 + (y - k)^2 = r^2. |

characteristic | The characteristic equation of the differential equation is 4x^2-20x+25=0. |

second | Solve for the variables in the second equation |

integral | The two-dimensional integral equation is solved by successive approximations. |

simple | The simple equation 2 + 2 = 4, is a great example of the basics of mathematics. |

single | The single equation was the solution to the complex problem. |

quadratic | The quadratic equation ax^2 + bx + c = 0 has two solutions, given by the quadratic formula. |

basic | The basic equation for motion is F = ma. |

partial | The partial equation is a mathematical equation that involves partial derivatives of the unknown function. |

personal | The personal equation between the two leaders was frosty. |

last | We plugged in our values for the last equation |

fundamental | The fundamental equation of thermodynamics describes the relationship between heat, work, and changes in internal energy in a thermodynamic system. |

original | The original equation is still the same. |

nonlinear | Solving the nonlinear equation was quite a challenge. |

corresponding | The corresponding equation is $y = 2x + 1$. |

dimensional | The dimensional equation is a mathematical equation that expresses the equality of two or more physical quantities expressed in terms of their dimensions. |

mathematical | The mathematical equation was so complex that it took me hours to solve it. |

ordinary | "Find out the first-order partial derivatives of the given first-order ordinary equation" |

constitutive | The constitutive equation for an elastic material is a mathematical relationship between stress and strain. |

empirical | Empirical equations are derived by means of applying data. |

homogeneous | The function f(x) satisfies a homogeneous equation if f(cx) = c^r f(x), where c is a constant and r is a rational number. |

balanced | The balanced equation shows the number of atoms of each element on both sides of the equation is equal. |

kinetic | The kinetic equation describes the time evolution of the particle velocity distribution function. |

third | The third equation in the system is x + y = 5. |

final | The final equation is obtained by solving the differential equation. |

cubic | The cubic equation has three real roots. |

dirac | The Dirac equation is a relativistic wave equation that describes the behavior of electrons and other subatomic particles. |

multiple | This problem has multiple equations and is difficult to solve. |

arrhenius | The Arrhenius equation describes the temperature dependence of reaction rates. |

order | Solve the third order equation |

structural | The results of the structural equation modeling revealed significant effects of gender on career satisfaction. |

appropriate | The appropriate equation to use depends on the specific problem you are trying to solve. |

generalized | The generalized equation for the reaction is A + B -> C |

logistic | The logistic equation models population growth with limited resources. |

functional | A functional equation is an equation that involves a function and its values. |

classical | The equation of a circle is a classical equation |

modified | The modified equation was able to accurately predict the results of the experiment. |

secular | The secular equation of the matrix is a polynomial equation whose roots are the eigenvalues of the matrix. |

dependent | The dependent equation needs to be solved in terms of the independent equations. |

dynamic | The dynamic equation governs the motion of the system. |

exact | |

latter | The latter equation is used to calculate the force of gravity. |

stochastic | The stochastic equation describes the evolution of a random variable over time. |

standard | Solve for x in the standard equation 3x + 5 = 14. |

linearized | The linearized equation which is also called a linear approximation, is a differential equation that is derived from the original equation by making a first-order Taylor expansion around a certain point. |

ideal | The ideal equation of state is a mathematical equation that describes the behavior of a gas under idealized conditions. |

complex | The complex equation was too difficult for me to solve. |

overall | The overall equation for the reaction is: 2H2 + O2 → 2H2O. |

hasselbalch | The Hasselbalch equation is used to calculate the pH of a solution. |

exponential | The exponential equation e^x = 2x can be solved using the Lambert W function. |

independent | The independent equation is the equation that does not depend on other equations. |

two | The two equations are equivalent. |

parabolic | The parabolic equation describes the motion of a projectile under the influence of gravity. |

known | The density equation is a known equation |

famous | Physicists are familiar with the famous equation E=mc^2 |

transcendental | The transcendental equation was highly complex and took many years to solve. |

theoretical | The theoretical equation for the trajectory of the projectile is y = -0.5 * g * t^2 + v0 * t + h. |

relativistic | The relativistic equation E = mc^2 is one of the most famous equations in physics. |

simultaneous | Simultaneous equation is a useful concept in mathematics. |

fourth | I don't know the fourth equation |

net | The net equation for the reaction is given by CO + O2 → CO2. |

radial | The radial equation is a differential equation that describes the radial part of the wavefunction of an electron in an atom. |

foregoing | The foregoing equation calculates the area of a circle. |

familiar | The familiar equation of the area of a circle was on the blackboard. |

thermal | The thermal equation was used to calculate the heat transfer between the two surfaces. |

state | The state equation describes the relationship between the pressure, volume, and temperature of a gas. |

implicit | The implicit equation x^2 + y^2 - 4 = 0 represents a circle with a radius of 2. |

inhomogeneous | The inhomogeneous equation can be solved using the method of undetermined coefficients. |

diffusion | The diffusion equation describes how a substance spreads out over time. |

hydrostatic | The hydrostatic equation is a fundamental equation in fluid mechanics that describes the pressure at any point in a fluid. |

called | |

equivalent | The equivalent equation of x2 - 5x - 6 = 0 is (x - 6)(x 1) = 0. |

simplified | The simplified equation is much easier to understand. |

correct | The answer is correct equation |

auxiliary | The auxiliary equation of the given differential equation is obtained by replacing (y), (rac{dy}{dx}), and (rac{d^2y}{dx^2}) with (m), (m^2), and (m^3), respectively. |

elliptic | The elliptic equation can be used to model various physical phenomena. |

lagrange | The Lagrange equation is a differential equation that describes the motion of a dynamical system. |

polar | The polar equation of a circle with radius r and center at the origin is r = a constant. |

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