GATE EE 2024 Set 1 — Question 45
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Engineering Mathematics → Differential Equations → First-Order Equations
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Question
Which of the following differential equations is/are nonlinear?
Correct answer
(B) (1)/(2) e^t + x(t) (dx(t))/(dt) = 0, x(0) = 0; (D) x(t) + e^(((dx(t))/(dt))) = 1, x(0) = 0
Solution
A differential equation is linear if the dependent variable and its derivatives appear only to the first power and are not multiplied together.
- (A): . This is a first-order linear differential equation of the form .
- (B): . This is nonlinear because of the product term involving the dependent variable and its derivative.
- (C): . This is a first-order linear differential equation.
- (D): . This is nonlinear because the derivative appears as the argument of a transcendental function ().
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