Which of the following differential equations has y = x as one of its particular solution? y d x 2 - x 2 dx + xy = x y d x 2 + x dx + xy = x y d x 2 - x 2 dx + xy = 0 y d x 2 + x 2 dx + xy = 0

Option c is correct We have y = x dx = 1 and y d x 2 = 0 which satisfy y d x 2 - x 2 dx + xy = 0 Exercise-9.4

Differential Equations — Class 12 Maths Solution

ncert exercise SA NCERT Ex.9.3,Q.12,Page 391

Question

Which of the following differential equations has $y = x$ as one of its particular solution?

• $\cfrac{{{d^2}y}}{{d{x^2}}} - {x^2}\cfrac{{dy}}{{dx}} + xy = x$

• $\cfrac{{{d^2}y}}{{d{x^2}}} + x\cfrac{{dy}}{{dx}} + xy = x$

• $\cfrac{{{d^2}y}}{{d{x^2}}} - {x^2}\cfrac{{dy}}{{dx}} + xy = 0$

• $\cfrac{{{d^2}y}}{{d{x^2}}} + {x^2}\cfrac{{dy}}{{dx}} + xy = 0$

Step-by-step Solution

Option c is correct

We have $y = x \Rightarrow \cfrac{{dy}}{{dx}} = 1$ and $\cfrac{{{d^2}y}}{{d{x^2}}} = 0$

which satisfy $\cfrac{{{d^2}y}}{{d{x^2}}} - {x^2}\cfrac{{dy}}{{dx}} + xy = 0$

Exercise-9.4

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Differential Equations. Curated by Sachin Sharma. Free for all students.