Differential Equations Question 1
Question: The equation of the curve which passes through the point (1, 1) and whose slope is given by $ \frac{2y}{x} $ , is
[Roorkee 1987]
Options:
A) $ y=x^{2} $
B) $ x^{2}-y^{2}=0 $
C) $ 2x^{2}+y^{2}=3 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Slope $ \frac{dy}{dx}=\frac{2y}{x} $
Therefore $ 2\int{\frac{dx}{x}}=\int{\frac{dy}{y}} $
Therefore $ 2\log x=\log y+\log c $
Therefore $ x^{2}=yc $
Since it passes through (1, 1), therefore $ c=1 $
Hence $ x^{2}-y=0 $
Therefore $ y=x^{2} $ .
BETA
