MTH232
The sufficient conditions for existence of solution of the first order equation \(\\frac{dy} {dx}=f(x,y)\), with \(y(x_0 )=y_0\) in a region T defined by\( |x-x_0 |<a\) and \(|y-y_0 |<b\) are
Answer: f is continuous in t and f is bounded in t
An equation of the form \(\\frac{dy} (dx}=f(x,y)\) is called a
Answer: separable equation
Any solution which is obtained from the general solution by giving particular values to the arbitrary constraint is called a
Answer: particular solution
Conditions on the value of the dependent variable, and its derivatives, at a single value of the independent variable in the interval of existence of the solution are called the
Answer: initial conditions.
The coefficients of a are either constant or functions of the independent variable or variables.
Answer: linear equation
is an ordinary linear differential equation.
Answer: \\(\\frac{d^2y}{dx^2}+y=x^2\\)
A solution of a differential equation which cannot be obtained by assigning definite values to the arbitrary constraints in the general solution is called its
Answer: singular solution
The coefficients of a are either constant or functions of the independent variable or variables.
Answer: linear equation
The problem of doing a differential equation together with initial conditions is called the
Answer: initial value problem
is an example of nonlinear differential equation.
Answer: \\((x+y)A2\\frac{dy}{dx}=1\\)
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