Question:
The solution of the differential equation \(x^2\,dx+y^2\,dy=0\) is
The solution of the differential equation \(x^2\,dx+y^2\,dy=0\) is
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Form \(M(x)dx+N(y)dy=0\) \(\Rightarrow\) integrate terms independently.
Updated On: Oct 17, 2025
- \(x^3+y^3=k\)
- \(x^2+y^2=k\)
- \(x^2-y^2=k\)
- \(x^2-y^2=k\)
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The Correct Option is A
Solution and Explanation
Idea. This is already separated: an \(x\)-part with \(dx\) plus a \(y\)-part with \(dy\). Integrate each side straight away.
\[ \int x^2\,dx+\int y^2\,dy=C $\Rightarrow$ \frac{x^3}{3}+\frac{y^3}{3}=C $\Rightarrow$ x^3+y^3=k. \]
\[ \int x^2\,dx+\int y^2\,dy=C $\Rightarrow$ \frac{x^3}{3}+\frac{y^3}{3}=C $\Rightarrow$ x^3+y^3=k. \]
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