Differential Equation MCQ Level - 1 - IIT JAM MCQ

The given differential equation is homogeneous
Consider,

Comparing it with the equation

We have,  

Also, the equation is homogeneous &

∴  The integrating factor would be given by

The correct answer is: x

Given,

Replacing   to get the orthogonal curve,

Integrating both sides

The correct answer is: 

which is a linear equation

The required solution will be given by

The correct answer is:
5y = x⁴ + ax^–1

Consider the differential equation,

Cubing both sides,

∴  according to definition, degree of the above differential equation is 3 and order is 2.

The correct answer is: Order–2 & Degree–3

We have 

Putting   the above equations becomes

Auxiliary equation : 

Hence, 

The correct answer is: 

Since y = e^x is an integral, we take y = ve^x 

The given equation becomes

Hence y = ve^x = (c₁ log x + c₂)e^x is the complete solution.

The correct answer is: (C₁ log x + C₂)e^x

Multiplying the given equation by x² we obtain

Then the equation, on putting   becomes

The correct answer is: 

Comparing it with the equation,
Mdx + Ndy = 0
We have,
         M = y cos x + sin y + y    &     N = sin x + x cos y + x

Hence, the given differential equation is exact.
∴  The required solution will be given by,

The correct answer is: y sin x + (sin y + y) x = c

We have P + Qx = –x² + x² = 0 and so y = x is an integral.

Let y = vx so that  

Now the given equation reduces to

On putting    the given equation becomes

The auxiliary equation is  


Hence,   is the solution: 

The correct answer is: