GATE EC 2014 Set 3 — Question 12
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Engineering Mathematics → Differential Equations → First-Order Linear Equations
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Question
Which ONE of the following is a linear non-homogeneous differential equation, where and are the independent and dependent variables respectively?
Correct answer
(A) (dy)/(dx) + xy = e^(-x)
Solution
A first-order linear differential equation is of the form . It is non-homogeneous if .
(A) is linear () and non-homogeneous ().
(B) is linear but homogeneous ().
(C) is non-linear because the dependent variable appears in the exponent of .
(D) is non-linear because of the term.
(A) is linear () and non-homogeneous ().
(B) is linear but homogeneous ().
(C) is non-linear because the dependent variable appears in the exponent of .
(D) is non-linear because of the term.
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