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Engineering Mathematics
Differential Equations

Practice questions from Differential Equations.

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Q#1 Differential Equations GATE EC 2025 (Set 1) NAT +1 mark -0 marks

The function  satisfies

 

where  and  denote the first and second derivatives of  respectively.

Given  and , the maximum value of  over  is _________ (rounded off to two decimal places).

Explanation:

Given:

 

Given differential equation is of the form of Cauchy-Euler equation.

 

 

The equation reduces to :

 

 

 

Its, auxiliary equation is

 

 

 

   

 

Put ,  

 

 

stationary point:    

 point of Maxima

 

 

Q#2 Differential Equations GATE EC 2024 (Set 1) MCQ +1 mark -0.33 marks

The general form of the complementary function of a differential equation is given by where A and B are real constants determined by the initial condition. The corresponding differential equation is__________.

Explanation:

Based on the solution we can judge that the characteristic equation has repeated real roots