CUET · MATHS · PYQ PAPER 2025
The particular solution of the differential equation \(\frac{d y}{d x}=8 y x\) when \(y=1\) at \(x=0\) is:
- A \(y=e^{x^2}\)
- B \(y=e^{4 x^2}\)
- C \(y=e^{8 x^2}\)
- D \(y=e^x\)
Answer & Solution
Correct Answer
(B) \(y=e^{4 x^2}\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{y} = 8x \, dx\) \(\int \frac{d y}{y} = \int 8x \, dx\) \(\ln|y| = 4x^2 + C\) \(y = A e^{4x^2}\) \(1 = A e^{4(0)^2} \Rightarrow A = 1\) \(y = e^{4x^2}\)
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