Subtopic: Linear and non-linear first order Ordinary Differential Equations (ODE)
Question Statement:
The differential equation 2(d²z/dx²) + dz/dx + 3y = sin x is considered to be ordinary, as it has
Options:
(A) one dependent variable
(B) more than one dependent variable
(C) one independent variable
(D) more than one independent variable
Official Answer Key:
C
Step-by-Step Solution & Explanation
An ODE (ordinary differential equation) involves derivatives with respect to only one independent variable. Here every derivative (d²z/dx², dz/dx) is taken with respect to x alone, so x is the sole independent variable — this is exactly what makes the equation 'ordinary' rather than partial. (Note the equation itself is unusual in mixing z and y, but the classification test asked for is purely about the number of independent variables.) Options (A)/(B) test dependent-variable count, which is irrelevant to the ODE/PDE distinction; (D) is the direct opposite of the correct property.
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