Question

.
Solve (d2 y/ dx?) + y = 0, given y =2 for x = 0 and y=-2 for x = =+.
(Avadh 05)
11.
1
=
2​

Answer 1

Answer:

(i) An equation involving derivative (derivatives) of the dependent variable with

respect to independent variable (variables) is called a differential equation.

(ii) A differential equation involving derivatives of the dependent variable with

respect to only one independent variable is called an ordinary differential

equation and a differential equation involving derivatives with respect to more

than one independent variables is called a partial differential equation.

(iii) Order of a differential equation is the order of the highest order derivative

occurring in the differential equation.

(iv) Degree of a differential equation is defined if it is a polynomial equation in its

derivatives.

(v) Degree (when defined) of a differential equation is the highest power (positive

integer only) of the highest order derivative in it.

(vi) A relation between involved variables, which satisfy the given differential

equation is called its solution. The solution which contains as many arbitrary

constants as the order of the differential equation is called the general solution

and the solution free from arbitrary constants is called particular solution.

(vii) To form a differential equation from a given function, we differentiate the

function successively as many times as the number of arbitrary constants in the

given function and then eliminate the arbitrary constants.

(viii) The order of a differential equation representing a family of curves is same as

the number of arbitrary constants present in the equation corresponding to the

family of curves.

(ix) ‘Variable separable method’ is used to solve such an equation in which variables

can be separated completely, i.e., terms containing x should remain with dx and

terms containing y should remain with dy.