40.7.7 problem 16

Internal problem ID [6697]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 12. Linear equations of order n. Supplemetary problems. Page 81
Problem number : 16
Date solved : Monday, January 27, 2025 at 02:24:16 PM
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: 0.002 (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: 0.020 (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]
 

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