7.17.3 problem 3

Internal problem ID [516]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.6 (Applications of Bessel functions). Problems at page 261
Problem number : 3
Date solved : Wednesday, February 05, 2025 at 03:42:15 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x y^{\prime \prime }-y^{\prime }+36 x^{3} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(x*diff(y(x),x$2)-diff(y(x),x)+36*x^3*y(x)=0,y(x), singsol=all)
 

\[ y = c_1 \sin \left (3 x^{2}\right )+c_2 \cos \left (3 x^{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 24

DSolve[x*D[y[x],{x,2}]-D[y[x],x]+36*x^3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cos \left (3 x^2\right )+c_2 \sin \left (3 x^2\right ) \]