DQ **Question 2**The solution of the differential equation $ x^2 y'' - 3xy' + 4y = 0 $ is Select the correct answer.- a. $ y = c_1 x^{\frac{3+\sqrt{7}}{2}} + c_2 x^{\frac{3-\sqrt{7}}{2}} $- b. $ y = c_1 x^2 + c_2 x^2 \ln x $- c. $ y = c_1 x + c_2 x \ln x $- d. $ y = c_1 x + c_2 x^2 $- e. $ y = c_1 x + c_2 x^3 $

Answered: QUESTION 2 The solution of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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In this question, concept of Euler Type Differential Equation is used.

Euler Type Differential Equation

A linear homogeneous ordinary differential equation with variable coefficients is known as an Euler–Cauchy equation, Cauchy–Euler equation, or simply Euler's equation in mathematics. An equidimensional equation is another name for it. The differential equation can be solved explicitly due to its particularly simple equidimensional structure.

Euler Equations gives solutions to following equation around $x_{0} = 0$ .

$a x^{2} y'' + b x y' + c y = 0$