Consider the second-order differential equation .
Using the method of Frobenius, which of these is the general solution of this differential equation? Assume are arbitrary real constants.
A) $ y(x)=a_{0}+a_{0}^{*}\left(x \ln x+\sum_{n=1}^{\infty} \frac{(-1)^{n} x^{n+1}}{n \cdot n !}\right) $
B) $ y(x)=a_{0} x+a_{0}^{*}\left(x \ln x+\sum_{n=1}^{\infty} \frac{(-1)^{n} x^{n+1}}{n \cdot n !}\right) $
C) $ y(x)=a_{0}+a^{*}{ }_{0}^{x}\left[\ln x+\sum_{n=1}^{\infty} \frac{(-1)^{n} x^{n+1}}{n \cdot n !}\right) $
D) $ y(x)=a_{0}+a_{0}^{*} \ln x\left(1+\sum_{n=1}^{\infty} \frac{(-1)^{n} x^{n+1}}{n \cdot n !}\right) $

Question

Consider the second-order differential equation  .
Using the method of Frobenius, which of these is the general solution of this differential equation? Assume  are arbitrary real constants.
A) $ y(x)=a_{0}+a_{0}^{*}\left(x \ln x+\sum_{n=1}^{\infty} \frac{(-1)^{n} x^{n+1}}{n \cdot n !}\right) $ 
B) $ y(x)=a_{0} x+a_{0}^{*}\left(x \ln x+\sum_{n=1}^{\infty} \frac{(-1)^{n} x^{n+1}}{n \cdot n !}\right) $ 
C) $ y(x)=a_{0}+a^{*}{ }_{0}^{x}\left[\ln x+\sum_{n=1}^{\infty} \frac{(-1)^{n} x^{n+1}}{n \cdot n !}\right) $ 
D) $ y(x)=a_{0}+a_{0}^{*} \ln x\left(1+\sum_{n=1}^{\infty} \frac{(-1)^{n} x^{n+1}}{n \cdot n !}\right) $

Quizplus · Accepted Answer

The Answer of Consider the second-order differential equation  .
Using the method of Frobenius, which of these is the general solution of this differential equation? Assume  are arbitrary real constants.
A) $ y(x)=a_{0}+a_{0}^{*}\left(x \ln x+\sum_{n=1}^{\infty} \frac{(-1)^{n} x^{n+1}}{n \cdot n !}\right) $ 
B) $ y(x)=a_{0} x+a_{0}^{*}\left(x \ln x+\sum_{n=1}^{\infty} \frac{(-1)^{n} x^{n+1}}{n \cdot n !}\right) $ 
C) $ y(x)=a_{0}+a^{*}{ }_{0}^{x}\left[\ln x+\sum_{n=1}^{\infty} \frac{(-1)^{n} x^{n+1}}{n \cdot n !}\right) $ 
D) $ y(x)=a_{0}+a_{0}^{*} \ln x\left(1+\sum_{n=1}^{\infty} \frac{(-1)^{n} x^{n+1}}{n \cdot n !}\right) $

Consider the Second-Order Differential Equation y(x)=a0+a0∗(xln⁡x+∑n=1∞(−1)nxn+1n⋅n!) y(x)=a_{0}+a_{0}^{*}\left(x \ln x+\sum_{n=1}^{\infty} \frac{(-1)^{n} x^{n+1}}{n \cdot n !}\right) y(x)=a0​+a0∗​(xlnx+∑n=1∞​n⋅n!(−1)nxn+1​)

Consider the Second-Order Differential Equation $y(x)=a_{0}+a_{0}^{*}\left(x \ln x+\sum_{n=1}^{\infty} \frac{(-1)^{n} x^{n+1}}{n \cdot n !}\right)$