Question

The differential equation which represents the family of curves y = e^Cx is

Options

• y₁ = C² y

• xy₁ − ln y = 0

• x ln y = yy₁

• y ln y = xy₁

Answer 1

y ln y = xy₁

 

We have,
y = e^Cx
Taking ln on both sides, we get
ln y = Cx ln e
⇒ In y = Cx                     ........(1)
Differentiating both sides of (1) with respect to x, we get
\[\frac{1}{y} y_1 = C\]
Substituting the value of C in (1), we get
\[\ln y = \frac{y_1}{y}x\]
\[ \Rightarrow y \ln y = y_1 x\]