NDA 2017 Paper 1 | Differential Equations Question 14 | Mathematics

What are the degree and order respectively of the differential equation $$y = x{\left( {{{dy} \over {dx}}} \right)^2} + {\left( {{{dx} \over {dy}}} \right)^2}$$ ?

1, 2

2, 1

1, 4

4, 1

NDA 2017 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

What is the differential equation corresponding to $${y^2} - 2ay + {x^2} = {a^2}$$ by eliminating a?

$$({x^2} - 2{y^2}){p^2} - 4pxy - {x^2} = 0$$

$$({x^2} - 2{y^2}){p^2} + 4pxy - {x^2} = 0$$

$$({x^2} + 2{y^2}){p^2} - 4pxy - {x^2} = 0$$

$$({x^2} + 2{y^2}){p^2} - 4pxy + {x^2} = 0$$

NDA 2017 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

What is the general solution of the differential equation $$ydx - (x + 2{y^2})dy = 0$$ ?

$$x = {y^2} + Cy$$

$$x = 2C{y^2}$$

$$x = 2{y^2} + Cy$$

None of these

NDA 2017 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

What is the solution of the differential equation $$\ln \left( {{{dy} \over {dx}}} \right) - a = 0$$ ?

$$y = x{e^a} + C$$

$$x = y{e^a} + C$$

$$y = \ln x + C$$

$$x = \ln y + C$$

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