Question

Solve (x2D2 – xD – 2)y = x2 log x.​

Answer 1

Answer:

find by using property 1254525x(-25)+125x75

56Step-by-step explanation:

Answer 2

Concept:-

It might resemble a word or a number representation of the quantity's arithmetic value. It could resemble a word or a number that represents the numerical value of the quantity. It could have the appearance of a word or a number that denotes the quantity's numerical value.

Given:-

Given that "Solve $(x2D2 - xD - 2)y = x2 log x$.​"

Find:-

We need to find the value of "Solve $(x2D2 - xD - 2)y = x2 log x$.​"

Explanation:-

The given equation is

Substitute $x=e^z$ or $z=logx$ in equation one

Then $x\frac{dy}{dx}=Dy$, and  $x^2\frac{d^2y}{dx^2}=D(D-1)y$

Equation one reduces to,

$D(D-1)y-Dy+y=2z$

i.e., $(D^2-2D+1)y=2z......(2)$

which is an equation with constant coefficients

A.E. is $m^2-2m+1=0$

i.e., $(m-1)^2=0$

$\therefore m=1$,$1$

C.F. $=(C_1+C_2z)e^z$

P.I.

$=\frac{1}{D^2-2D+1}2z \\=2z+4$

$x^2d^2y/dx^2 - xdy/dx + y = 2logx$

$\therefore$ The general solution of Eqn. $(2)$ is  $y = (C_1 + C_2z) e^z + 2z + 4$

Hence, the general solution of $(x2D2 - xD - 2)y = x2 log x$ is  $y = (C_1 + C_2z) e^z + 2z + 4$.

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