Question
Let y=y(x) be the solution of the differential equation x ~d y ~d x -y=x^ 2 x, x (0, ). If y ( 2 )= 2 , then 6 y ( 6 )-8 y ( 4 ) is equal to :
JEE Main
Mathematics
Differential Equations
2026
JEE Main 2026 (28 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 3
- B.
- C. -
- D. -3
Answer
C. -
Step-by-step solution
The differential equation x dy dx - y = x^2 x can be rewritten as dy dx - y x = x x. The integrating factor is (x) = 1 x . Multiplying by (x) gives d dx ( y x ) = x. Integrating: y x = | x| + C, so y = x ( x) + Cx. Using y ( 2 ) = 2 : we get 2 = 0 + C 2 , thus C = 1. Therefore y = x(1 + ( x)). Now: y ( 6 ) = 6 (1 - 2) and y ( 4 ) = 4 (1 - 2 2 ). Thus 6y ( 6 ) - 8y ( 4 ) = (1 - 2) - 2 (1 - 2 2 ) = - .
Related: Mathematics — Differential Equations · All PYQ Banks