Question
Question: If y = (x) is the equation of the curve and its differential equation is given by \(\frac{dy}{dx}\)...
If y = (x) is the equation of the curve and its differential equation is given by dxdy= y+3x+2, then the equation of the curve, if it passes through (2, 2), is –
A
x2 – y2 + 4x – 6y + 4 = 0
B
x2 – y2 + 4x + 6y = 0
C
x2 – y2 – 4x – 6y = 0
D
x2 – y2 – 4x – 6y – 4 = 0
Answer
x2 – y2 + 4x – 6y + 4 = 0
Explanation
Solution
The given equation is (y + 3) dy = (x + 2) dx
Ž 2y2 + 3y = 2x2 + 2x + c
Since, it passes through (2, 2)
\ 2 + 6 = 2 + 4 + c Ž c = 2 \ 2y2 + 3y = 2x2 + 2x + 2 Ž y2 + 6y = x2 + 4x + 4
Ž x2 + 4x – y2 – 6y + 4 = 0