### Find the particular solution that satisfies the differential equation and the initial condition.

f”(x) = sin (x) , f'(0) = 1,  f(0) = 6 This problem aims to familiarize us with the concepts of initial value problems. The concepts required to solve this problem are related to the basics […]

### If xy+8e^y=8e , find the value of y” at the point where x=0.

This question aims to find the value of the second derivative of the given non-linear equation.  Nonlinear equations are those which show up as curved lines when graphed. The degree of such an equation is two or more, but not less than two. The curvature of the graph increases as the value of the degree […]

### If xy+6e^y=6e, find the value of y” at the point where x=0.

This question aims to find the second derivative of the given implicit function. A function’s derivatives describe the rate of change of that function at a given point. If the dependent variable, say $y$, is a function of the independent variable, say $x$, we usually express $y$ in terms of $x$. When this occurs, $y$ […]

### Each limit represents the derivative of some function f at some number a.

Find the number $a$ and the function $f$ given the following limit: [lim_{tto 1} frac{t^4 + t – 2}{t-1}] The aim of this question is to learn the differentiation (calculation of derivative) from first principles (also called by definition or by ab-initio method). To solve this question, one needs to know the basic definition of […]

### Find transient terms in this general solution to a differential equation, if there are any

$y=(x+C)(dfrac{x+2}{x-2})$ This article aims to find the transient terms from the general solution of the differential equation. In mathematics, a differential equation is defined as an equation that relates one or more unknown functions and their derivatives. In applications, functions generally represent physical quantities, derivatives represent their rates of change, and a differential equation defines the relationship between them. Such […]