DIFFERENTIAL EQUATIONS

standard form for a pair of ordinary simultaneous equation of the first order but first degree

• dx/p=dY/Q=dz/R

• dx/l=dy/m=dz/n

• dx/p=dy/Q=dz/R

• dx/l+dy/m+dz+n

Each ratio in equation dx/P=dy/Q=dz/R is equal to

• dx+dy+dz/P+Q+R

• ldx+mdy+ndz/lP+mQ+nR

• Pdx+Qdy+Rdz/p²+Q²+R²

• dx/P=dy/Q=dz/R

What is the general solution for the system of equations represented by dx/P=dy/Q=dz/R?

• dx=ldx+mdy+ndz

• dx/P=dy/Q=dz/R

• dx=Qdy+Rdz

• dx=ky+lz

In the equation dx/P=dy/Q=dz/R, what does the variable P represent?

• Ratio of changes in x

• Constant term

• Sum of all variables

• Coefficient of dx

Which of the following represents a condition for the existence of a unique solution in simultaneous equations?

• Determinant of coefficients is zero

• Determinant of coefficients is non-zero

• Sum of ratios equals one

• All variables are equal

What is the condition for a system of equations to have infinitely many solutions?

• All equations are independent

• Determinant of coefficients is zero

• At least one equation is redundant

• Determinant of coefficients is non-zero

Which of the following forms represents a linear combination of variables in a system of equations?

• e^{x+y} = z

• x^2 + y^2 = r^2

• xy + z = k

• ax + by + cz = d

In the context of simultaneous equations, what does the term 'homogeneous' refer to?

• Equations have no solutions

• All terms are equal

• All variables are positive

• All constant terms are zero