52.3.24 problem 26

Internal problem ID [8310]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. 6.4 SPECIAL FUNCTIONS. EXERCISES 6.4. Page 267
Problem number : 26
Date solved : Monday, January 27, 2025 at 03:48:36 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{2}+3\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 21

dsolve(4*x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+(16*x^2+3)*y(x)=0,y(x), singsol=all)
 

\[ y = \sqrt {x}\, \left (c_{1} \sin \left (2 x \right )+c_{2} \cos \left (2 x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 39

DSolve[4*x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+(16*x^2+3)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} e^{-2 i x} \sqrt {x} \left (4 c_1-i c_2 e^{4 i x}\right ) \]