AP EAMCET · Maths · Differential Equations
If \(x^2 y-x^3 \frac{d y}{d x}=y^4 \cos x\), then \(x^3 y\) is equal to
- A \(\sin x\)
- B \(2 \sin x+c\)
- C \(-3 \sin x+c\)
- D \(3 \cos x+c\)
Answer & Solution
Correct Answer
(C) \(-3 \sin x+c\)
Step-by-step Solution
Detailed explanation
Given that \(x^2 y-x^3 \frac{d y}{d x}=y^4 \cos x\) On dividing by \(y^4\), we get \(\begin{aligned} \frac{x^2}{y^3}-\frac{x^3}{y^4} \frac{d y}{d x} & =\cos x \\ \Rightarrow \quad \frac{x^3}{y^4} \frac{d y}{d x} & =\frac{x^2}{y^3}-\cos x\end{aligned}\)…
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