AP EAMCET · Maths · Differential Equations
If the solution of \(\frac{d y}{d x}=\frac{y^3 \cos \sqrt{x}}{\sqrt{x} e^{1 / y^2}}, y(0)=1\) is \(\frac{1}{y^2}=\log _e(f(x))\), then \(f(x)=\)
- A \(4+4 \sin \sqrt{x}\)
- B \(e \sin \sqrt{x}\)
- C \(1-4 \sin \sqrt{x}\)
- D \(e-4 \sin \sqrt{x}\)
Answer & Solution
Correct Answer
(D) \(e-4 \sin \sqrt{x}\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}=\frac{y^3 \cos \sqrt{x}}{\sqrt{x} e^{1 / y^2}}\) \(\Rightarrow \int \frac{e^{1 / y^2}}{y^3} d y=\int \frac{\cos \sqrt{x}}{\sqrt{x}} d x\) On putting \(\frac{1}{y^2}=t \Rightarrow-\frac{2}{y^3} d y=d t\) and on putting…
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