CUET · MATHS · PYQ PAPER 2023
The solution of the differentiable equation \(2 x \frac{d y}{d x}+y=14 x^3, x>0\), is:
- A \(y=2 x^3+c x^{\frac{1}{2}}\)
- B \(y=x^3+c x^{\frac{1}{2}}\)
- C \(y=2 x^3+c x^{-\frac{1}{2}}\)
- D \(y=x^3+c x^{-\frac{1}{2}}\)
Answer & Solution
Correct Answer
(C) \(y=2 x^3+c x^{-\frac{1}{2}}\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}+\frac{1}{2 x} y=7 x^2\) \(IF = e^{\int \frac{1}{2 x} d x} = e^{\frac{1}{2} \ln x} = x^{\frac{1}{2}}\) \(y \cdot x^{\frac{1}{2}} = \int 7 x^2 \cdot x^{\frac{1}{2}} d x + C\) \(y x^{\frac{1}{2}} = \int 7 x^{\frac{5}{2}} d x + C\)…
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