Question
( d y d x ) x=y ^2 x+ x, find general solution
BITSAT
Mathematics
Differential Equations
2022
BITSAT 2022
BITSAT Mathematics Question (2022) — Solution
Options
- A. y= x( | cosec x- x|+ x+c)
- B. y= ^2 x+ x+c
- C. y= | x+ x|+ cosec x+c
- D. y= ^2 x+ x+c
Answer
A. y= x( | cosec x- x|+ x+c)
Step-by-step solution
Given that aligned & ( d y d x ) x=y ^2 x+ x \\ & x ( d y d x )-y ^2 x= x \\ & d y d x + ( - ^2 x x ) y= x x \\ & Here, P=- ^2 x x and Q= x \\ & IF =e^ P d x =e^ - ^ 2 x x d x \\ & IF =e^ - ( x) =e^ x = x \\ & Now, y IF = (Q IF ) d x+C \\ & y x= x x+C \\ & y x= 1- ^2 x x +C \\ & y x= | cosec x- x|+ x+C aligned
Related: Mathematics — Differential Equations · All PYQ Banks