Question
If the slope of the tangent to the curve at any point P (x, y) is y x - ^ 2 y x , then the equation of a curve passing through (1, 4 ) is
BITSAT
Mathematics
Differential Equations
2021
BITSAT 2021
BITSAT Mathematics Question (2021) — Solution
Options
- A. ( y x )+ x=1
- B. ( y x )+ y=1
- C. ( x y )+ x=1
- D. ( x y )+ y=1
Answer
A. ( y x )+ x=1
Step-by-step solution
According to the condition, dy dx = y x - ^ 2 y x (i) This is a homogeneous differential equation Substituting y=v x, we get array l v+x dv dx =v- ^ 2 v \\ x dv dx =- ^ 2 v \\ ^ 2 vdv =- dx x \\ v=- x+ C \\ y x + x= C array Substituting x =1, y= 4 , we get C =1 Thus, we get ( y x )+ x=1 which is the required solution.
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