Subtopic: Linear and non-linear first order Ordinary Differential Equations (ODE)
Question Statement:
y″ + p(x)y′ + q(x)y = r(x) is a ________ ordinary differential equation.
Options:
(A) second order, nonhomogeneous, and linear
(B) second order, homogeneous, and linear
(C) second order, homogeneous, and nonlinear
(D) first order, nonhomogeneous, and linear
Official Answer Key:
A
Step-by-Step Solution & Explanation
Highest derivative present is y″ → second order. y and its derivatives appear only to the first power with coefficients depending on x → linear. Since r(x) ≠ 0 (in general) the equation is nonhomogeneous.
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