A) Both statements are false.
B) Statement 1 is rue and statement 2 is false.
C) Statement 1 is false. Statement 2 is true
D) Both statement s are true.
Correct Answer: D
Solution :
Give differential equation is \[\frac{dy}{dx}=\frac{{{y}^{3}}}{2(xy-{{x}^{2}})}\] But substituting \[z={{y}^{2}},\]we get diff. eqn. as \[\frac{dz}{dx}=\frac{2{{z}^{2}}}{2(xz-{{x}^{2}})}=\frac{{{z}^{2}}}{xz-{{x}^{2}}}\] Now, \[\frac{dz}{dx}=\frac{2{{z}^{2}}}{2(xz-{{x}^{2}})}=\frac{{{z}^{2}}}{xz-{{x}^{2}}}\] Hence, statement -1 is true. Now, \[{{y}^{2}}{{e}^{-{{y}^{2}}/x}}=C\]satisfies the given diff. equation \[\therefore \] it is the solution of given diff. equation. Thus, statement -2 is also true.
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