LINEAR EQUATIONS IN ONE VARIABLE part 2

STATEMENT-1 : The differential equation (d^(2)y)/(dx^(2)) + cos x.(dy)/(dx) + (x^(3) + 7)y = e^(x) is a linear equation and STATEMENT-2 : Every first degree equation is a linear equation.

Divide 184 into two parts such that one-third of one part may exceed one-seventh of the other part by 8.

Divide 184 into two parts such that one-third of one part may exceed one-seventh of the other part by 8.

Which of the following statements on ordinary differential equations is/are true ? (i) The number of arbitrary constants is same as the degree of the differential equation. (ii) A linear differential equation can contain products of the dependent variable and its derivatives. (iii) A particular integral cannot contains arbitrary constants. (iv) By putting v=(y)/(x) any homogeneous first order differential equation transforms to variable separable form.

Solve for x and y, by reducing the following equations in a pair of linear equations : 2x + 3y = 5xy and 3x - 2y = xy.

If one angle of a linear pair is acute, then the other angle is

Find the value of k for which the point (1,\ -2) lies on the graph of the linear equation x-2y+k=0

If the point (a ,\ 2) lines on the graph of the linear equation 2x-3y+3=0 , find the value of a

3x-2-7,3/2x+9=1/2, y/3+(y-2)/4=5 are linear equations in one variable, because the highest power of the variable in each equation in one whereas the equations 3x^2-2x+1=0, y^2-1=8 are not linear equations, because the highest power of the variable in each equation is not one. In this chapter, we shall study linear equations in one variable only.

Every point on the graph of a linear equation in two variables does not represent a solution of the linear equation.