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JEE Mains · Maths · STD 12 - 9. differential equations
Consider the differential equation \(\frac{{dy}}{{dx}} = \frac{{{y^3}}}{{2(x{y^2} - {x^2})}}\) Statement \(-1:\) The substitution \(z = y^2\) transforms the above equation into a first order homogenous differential equation. Statement \(-2:\) The solution of this differential equation is \({y^2}{e^{ - {y^2}/x}} = C\).
- A Both statements are false.
- B Statement \(-1\) is true and statement \(-2\) is false.
- C Statement \(-1\) is false and statement \(-2\) is true.
- D Both statements are true.
Answer & Solution
Correct Answer
(D) Both statements are true.
Step-by-step Solution
Detailed explanation
Given differential equation is \(\frac{d y}{d x}=\frac{y^{3}}{2\left(x y^{2}-x^{2}\right)}\) By substituting \(z=y^{2},\) we get diff. eqn. as \(\frac{d z}{d x}=\frac{2 z^{2}}{2\left(x z-x^{2}\right)}=\frac{z^{2}}{x z-x^{2}}\) Now,…
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