AP EAMCET · Maths · Differential Equations
If \(y=A t^2+\frac{B}{t}\) (A,B are parameters) is general solution of the differential equation \(f(t) y^{\prime \prime}(t)+g(t) y^{\prime}(t)+h(t) y=0\) then \(2 f(t)+t^2 h(t)=\)
- A \(g(t)-h(t)\)
- B \(g(t)+f(t)\)
- C \(g(t) f(t)\)
- D \((f(t))^{g(t)}\)
Answer & Solution
Correct Answer
(C) \(g(t) f(t)\)
Step-by-step Solution
Detailed explanation
\(y_1 = t^2, y_2 = t^{-1}\) \(y_1' = 2t, y_2' = -t^{-2}\) \(y_1'' = 2, y_2'' = 2t^{-3}\) \(\begin{vmatrix} y & t^2 & t^{-1} \\ y' & 2t & -t^{-2} \\ y'' & 2 & 2t^{-3} \end{vmatrix} = 0 \Rightarrow y(4t^{-2} + 2t^{-2}) - t^2(2y't^{-3} + y''t^{-2}) + t^{-1}(2y' - 2ty'') = 0\)…
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