JEE Mains · Maths · STD 12 - 9. differential equations
If \(y=y(x)\) is solution of the differential equation \(x\frac{{dy}}{{dx}} + 2y = {x^2}\) satisfying \(y(1)=1\) then \(y\left( {\frac{1}{2}} \right)\) is equal to
- A \(\frac{7}{{64}}\)
- B \(\frac{1}{{4}}\)
- C \(\frac{49}{{16}}\)
- D \(\frac{13}{{16}}\)
Answer & Solution
Correct Answer
(C) \(\frac{49}{{16}}\)
Step-by-step Solution
Detailed explanation
\(x \frac{d y}{d x}+2 y=x^{2}\) \(\frac{d y}{d x}+\frac{2}{x} y=x\) This is linear differential equation in \(\frac{\mathrm{d} \mathrm{y}}{\mathrm{d} \mathrm{x}}\) Integrating factor \(=e^{\int \frac{2}{x} d x}=x^{2}\) Solution of differential equation is…
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