JEE 2023 — Mathematics PYQ

Di gayi equation hai:

Isko rearrange karne par:

Ab puri equation ko $y^2$ se divide kijiye:

Step 2: Substitution

Maana $v=y^{-1}=\frac{1}{y}$. Iska derivative hoga:

Ab equation ban jayegi:

Step 3: Integrating Factor (I.F.) nikalna

Yeh ek Linear Differential Equation hai ($\frac{dv}{dx}+Pv=Q$).

Step 4: General Solution

Step 5: Constant $C$ ki value nikalna

Hame diya hai $y(0)=1$. Yani jab $x=0$ tab $y=1$:

Toh final equation hui:

Step 6: $\beta$ ki value find karna

Hame diya hai $y(2\sqrt{2})=\beta$. Yani $x=2\sqrt{2}$ par $y=\beta$:

Isse exponential form mein convert karne ke liye:

Sahi option (2) hai.