Class 12

Math

Calculus

Differential Equations

If y=(x+1+x2−−−−−√)n, then (1+x2)d2ydx2+xdydx is

- n2y
- −n2y
- −y
- 2x2y

**Correct Answer: ** Option(a)

**Solution: **[a] y=(x+1+x2−−−−−√)n dydx=n(x+1+x2−−−−−√)n−1(1+12(1+x2)−1/2.2x); dydx=n(x+1+x2−−−−−√)n−1(1+x2−−−−−√+x)1+x2−−−−−√=n(1+x2−−−−−√+x)n1+x2−−−−−√ or 1+x2−−−−−√dydx=ny or 1+x2−−−−−√y1=ny(y1=dydx) Squaring, (1+x2)y12.n2y2 Differentiating, (1+x2)2y1y2+y12.2x=n2.2yy1 (Here,y2=d2ydx2) or (1+x2)y2+xy1=n2y