73.10.11 problem 15.4

Internal problem ID [15306]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 15. General solutions to Homogeneous linear differential equations. Additional exercises page 294
Problem number : 15.4
Date solved : Tuesday, January 28, 2025 at 07:52:04 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 20

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

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