MHT CET · Maths · Differential Equations
The differential equation which represents the family of curves \(\mathrm{y}=\mathrm{C}_1 \mathrm{e}^{\mathrm{c}_2 x}\), where \(\mathrm{C}_1, \mathrm{C}_2\) are arbitrary constants is
- A \(y^{\prime \prime}=y^{\prime} y\)
- B \(y y^{\prime \prime}=y^{\prime}\)
- C \(y y^{\prime \prime}=\left(y^{\prime}\right)^2\)
- D \(\mathrm{y}^{\prime}=\mathrm{y}^2\)
Answer & Solution
Correct Answer
(C) \(y y^{\prime \prime}=\left(y^{\prime}\right)^2\)
Step-by-step Solution
Detailed explanation
\(y = C_1 e^{C_2 x}\) \(y' = C_1 C_2 e^{C_2 x} = C_2 y\)
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