Explanation
Solution
1. Differential Equation ko standard form mein likhna:
Hume diya gaya hai:
Ise dxdy ke liye solve karte hain:
Ab x3 se divide karne par:
Ye ek Linear Differential Equation hai jo dxdy+P(x)y=Q(x) ke roop mein hai, jahan P(x)=x21 aur Q(x)=x31 hai.
2. Integrating Factor (I.F.) nikalna:
3. General Solution:
y⋅(I.F.)=∫Q(x)⋅(I.F.)dx+C
Is integral ko solve karne ke liye, maan lijiye −x1=t, toh x21dx=dt.
Saath hi, x31dx=x1⋅x21dx=−tdt.
Integral banta hai:
∫−tetdt=−(tet−et)=et(1−t)
Wapas t=−1/x rakhne par:
4. Constant C ki value nikalna:
Diya gaya hai y(21)=3−e:
3−e=3+Ce2⟹−e=Ce2⟹C=−e1=−e−1
Isliye solution hai:
y=1+x1−e−1e1/x=1+x1−e(1/x)−1
5. y(1) ki value:
Sahi Option: (A) 1
