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				   If y is a function of x then  (d2y/dx2) + y.(dy/dx) = 0.  If x is a function of y , then what does the same differential equation become ?


4 years ago

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										Solution:Let us assume a solution of the original differential equation as:$y=e^{ax}$Hence the given differential equation becomes:$a^{2}e^{ax}+ae^{2ax}=0 \Rightarrow e^{ax}=-a \Rightarrow y=\frac{logy}{x} \Rightarrow y^{1/y}=e^{x}$Thanks & RegardsSumit Majumdar,askIITians FacultyPh.D,IIT Delhi

one year ago

Integrate the following in terms of dx: (x^2 – 2x +3) / x^4

split (x^2 – 2x +3) / x^4 into: (x^-2 -2x^-3 + 3x^-4) dx = -x^-1 + x^-2 – x^-3 + c = -1/x + 1/x^2 – 1/x^3 + c

what are improper integrals? and what are the convergence of improper integrals ? why we want to study about this one ? where it will used?

IMPROPER INTEGRALS ARE THE DEFINITE INTEGRALS.IN IMPROPER INTEGRALS BOTH LIMITS OR UPPER OR LOWER LIMIT IS INFINITE IN THIS INTEGRATION THE VALUE WILL BE FINITE THAT IS CALLED CONVERGENT

 RAMCHANDRARAO 5 months ago

An improper integral is a definite i ntegral that has either or both limits infinite or an integrand that approaches infinity at one or more points in the range of integration.

 KALYAN 5 months ago

Dear Shivanand, Improper integral is definite integral which an infinite in lower and upper limits.And it can be solve from taking limits only.

 SAI SARDAR 5 months ago
Please it would be grateful if anybody could tell me the integration of xtan(x)dx

As it will result in the recursive equation and therefore it will be requried to convert into some special function.

 Vijay Mukati 10 months ago

I will try to provide it whenever I will be free. Thanks.

 Vijay Mukati 10 months ago

HIint. Please use the product rule for the integration here. Consider the x as 1 st term and tanx as second. Thanks.

 Vijay Mukati 10 months ago
who is father of analytic geometry???????????????????????????????

the father of analytic geometry ‘‘rene descartes’‘ is generally regarded as the father of analytical geometry.

 sudarshan 4 months ago

rene descarte...Descartes made significant progress with the methods in an essay titled (Geometry) , one of the three accompanying essays (appendices) published in 1637 together with his...

 T.kumar 4 months ago

Dear Gowri René Descartes (1596-1650) is generally regarded as the father of Analytical Geometry . His name in Latin is Renatius Cartesius — so you can see that our terminology “Cartesian...

 Prabhakar ch 4 months ago
Lim x->0 (xcosx-log(1+x))/x^2.Limx->0 (xcosx - x )/x^2 (by elimination )Lim x->0 (cosx - x)/xWhich is finally equal to zero but while using expansion and L hospital`s rule i get the answer...

Lim x->0 (xcosx-log(1+x))/x^2 from this to the below written statement Limx->0 (xcosx - x )/x^2 How you get this ??

 Sourabh Singh one month ago
what is the lenght of subtangent in the term of differential quotients of any general curve...

Let tangent and normal to a parabola at a point P(x1,y1) be extended to meet the axis of the parabola at N and T respectively. PT is termed the length of the tangent. PN is termed the length...

 Harsh Patodia 3 months ago
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