CUET · MATHS · PYQ PAPER 2025
The particular solution of the differential equation \(\left[\log \left(\frac{d y}{d x}\right)=3 x+4 y\right.\) satisfying \(y=0\) when \(x=0\) is :
- A \(3 e^{3 x}+4 e^{-4 y}+7=0\)
- B \(3 e^{3 x}-4 e^{-4 y}-7=0\)
- C \(4 e^{3 x}+3 e^{-4 y}-7=0\)
- D \(4 e^{3 x}-3 e^{-4 y}+7=0\)
Answer & Solution
Correct Answer
(C) \(4 e^{3 x}+3 e^{-4 y}-7=0\)
Step-by-step Solution
Detailed explanation
\(\log \left(\frac{d y}{d x}\right)=3 x+4 y\) \(\frac{d y}{d x}=e^{3x+4y} = e^{3x}e^{4y}\) \(e^{-4y} dy = e^{3x} dx\) \(\int e^{-4y} dy = \int e^{3x} dx\) \(-\frac{1}{4}e^{-4y} = \frac{1}{3}e^{3x} + C\) \(4e^{3x} + 3e^{-4y} = C'\) When \(x=0, y=0\):…
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