AP EAMCET · Maths · Differential Equations
If \(\mathrm{Ax}^3+\mathrm{Bxy}=4\) (A and B are arbitrary constants) is the general solution of the differential equation \(F(x) \frac{d^2 y}{d x^2}+G(x) \frac{d y}{d x}-2 y=0\), then \(F(1)+G(1)=\)
- A \(1\)
- B \(0\)
- C \(4\)
- D \(9\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
\(3Ax^2+By+Bx\frac{dy}{dx}=0\) \(6Ax+2B\frac{dy}{dx}+Bx\frac{d^2y}{dx^2}=0\) Substitute \(A=\frac{-By-Bx\frac{dy}{dx}}{3x^2}\) into the second equation: \(6x\left(\frac{-By-Bx\frac{dy}{dx}}{3x^2}\right)+2B\frac{dy}{dx}+Bx\frac{d^2y}{dx^2}=0\)…
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