JEE Mains · Maths · STD 12 - 9. differential equations
The general solution of the differential equation \(\left(x-y^{2}\right) d x+y\left(5 x+y^{2}\right) d y=0\) is.
- A \(\left( y ^{2}+ x \right)^{4}= C| \left( y ^{2}+2 x \right)^{3} \mid\)
- B \(\left( y ^{2}+2 x \right)^{4}= C| \left( y ^{2}+ x \right)^{3} |\)
- C \(\left|\left( y ^{2}+ x \right)^{3}\right|= C \left(2 y ^{2}+ x \right)^{4}\)
- D \(\left|\left(y^{2}+2 x\right)^{3}\right|=C\left(2 y^{2}+x\right)^{4}\)
Answer & Solution
Correct Answer
(A) \(\left( y ^{2}+ x \right)^{4}= C| \left( y ^{2}+2 x \right)^{3} \mid\)
Step-by-step Solution
Detailed explanation
\(\left(x-y^{2}\right) d x+y\left(5 x+y^{2}\right) d y=0\) \(\frac{d y}{d x}=\frac{y^{2}-x}{y\left(5 x+y^{2}\right)} .\) Let \(y^{2}=v\) \(\frac{2 y d y}{d x}=2\left(\frac{y^{2}-x}{5 x+y^{2}}\right)\) \(\frac{d v}{d x}=2\left(\frac{v-x}{5 x+v}\right) \quad v=k x\)…
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