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```                   Find the general solution of the differential equation:( (xlogx) dy/dx ) + y = (2/x) logx
```

3 years ago

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```                                        This is solved by integrating factor method.$\frac{\mathrm{d} y}{\mathrm{d} x}+y/(xlog(x))=2/x^2 \\=>\int 1/xlog(x)dx=log(log(x)) \\=>e^{log(log(x))}(\frac{\mathrm{d} y}{\mathrm{d} x}+y/(xlog(x))=2/x^2) \\=>e^{log(log(x))}*y=\int e^{log(log(x))}/x^2dx=\int log(x)/x^2dx=-e^{-log(x)}+c$Should be enough.Arun KumarIIT DelhiAskiitians Faculty
```
one year ago

inverse of f(x)=x3 + ex/2

the inverse of inverse of f(x)=x^3 + ex/2 is........ f^(-1) (x) = (sqrt(6) sqrt(54 x^2+e^3)+18 x)^(1/3)/6^(2/3)-e/(6^(1/3) (sqrt(6) sqrt(54 x^2+e^3)+18 x)^(1/3))

 Ajay Kotwal 2 months ago

good qustn..

 Ajay Kotwal 2 months ago

 Ajay Kotwal 2 months ago
See attachment sir please explain this question …...I’ll be very great full

Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty

 Arun Kumar one year ago

Differential of log ^n x is

 milind one year ago
I m having problem in these two questions: 1) f(x)=x^3+6x^2+(9+2k)x+1 is increasing if k is 2)f(x)=cosx-2PX is monotonically decreasing for p:

HInt: 1. If we diffirenciate a cubic equation, we get the quadratic equation. Not for cubic polynomial to be increasing function, its derivative should be positive, i.e. quadratic polynomial...

 Vijay Mukati one month ago
I was having trouble solving this question: If the coordinates of a point p be (aCosθ, bSinθ) whereθ is a variable quantity, find locuss of p. I really dont understand how to solve such...

the ans is (x/a) 2 +(y/b) 2 =1 it is simple u just need to eliminate θ and for that take x=acosθ and y=bsinθ so cosθ=x/a and sinθ=y/b now since cos 2 θ + sin 2 θ=1 we get (x/a) 2 +(y/b) 2...

 Nicho priyatham 2 months ago

Well that was simple! I guess I’ll just get some practice and would get a hang of it. Thanks!

 Jyotinder Singh 2 months ago
A repunit is a number that contains only the digit 1, and the repunit of n digits is denoted by r(n)= 11111...1111 there are total n1 If f(x)= 90x 2 +20x 2 +1 then find the sum of digits of ...

 ng29 3 months ago

it will be 21

i think 21

 Gman Namg 3 months ago
plz can u give me solution of q48 and q49

q49. Sn will be equal to coff. of x in : (1+1/x) n .(1+x) n = ∑ n C i * n C i+1 (that is power x i+1 from second bracket multiplied by power x i of first, and i varying from 0 to n-1....

 Akshay one month ago

will be the series in question. n . cofficient of x 2n-2i (-1) j (1+x) i C n = ∑ n -1) 2 q48. Assume ((x+1) Expand (x+1) 2 in LHS and solve. ATB.

 Akshay one month ago

q48. Assume ((x+1) 2 -1) n = ∑ n C i (1+x) 2n-2i . cofficient of x n will be the series in question. Expand (x+1) 2 in LHS and solve. ATB.

 Akshay one month ago
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