JEE Mains · Maths · STD 12 - 9. differential equations
If a curve \(y = f ( x )\) passes through the point \((1,2)\) and satisfies \(x \frac{d y}{d x}+y=b x^{4},\) then for what value of \(b, \int_{1}^{2} f(x) d x=\frac{62}{5} ?\)
- A \(5\)
- B \(10\)
- C \(\frac{62}{5}\)
- D \(\frac{31}{5}\)
Answer & Solution
Correct Answer
(B) \(10\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}+\frac{y}{x}=b x^{3}\) \(I . F .= e ^{\frac{1}{ x } dx }= x\) So, solution of \(D.E.\) is given by \(y \cdot x =\int b \cdot x ^{3} \cdot x d x + c\) \(y=\frac{c}{x}+\frac{b x^{4}}{5}\) Passes through \((1,2)\) \(2=c+\frac{b}{5}....(1)\)…
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