Question
If y=y(x) satisfies the differential equation 16( x+9 x )(4+ 9+ x ) y ~d y=(1+2 y) d x, x>0 and y(256)= 2 , y(49)= , then 2 is equal to :
JEE Main
Mathematics
Differential Equations
2026
JEE Main 2026 (22 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 2( 2 -1)
- B. 3( 2 -1)
- C. 2 2 -1
- D. 2 -1
Answer
C. 2 2 -1
Step-by-step solution
y 1+2 y d y= d x 16( 9 x +x )(4+ 9+ x ) 4+ 9+ x =t 1 2 9+ x d x 2 x =1 d x 1 2 n|1+2 y|= 4 d t 16 t +C . 1 2 n|1+2 y|= 1 4 n \, 4+ 9+ x +C 1 2 n(2 y+1)= 1 4 n|4+ 9+ x |+C Substituting (256, 2 ) 1 2 n 3= 1 2 n 3+C C=0 Substituting (49, ) 1 2 n (2 +1)= 1 4 n 8 n (2 +1)= 1 2 n 8 n (2 +1)= n 2 2 2 +1=2 2 2 =2 2 -1
Related: Mathematics — Differential Equations · All PYQ Banks