40.13.9 problem 29

Internal problem ID [6763]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 18. Linear equations with variable coefficients (Equations of second order). Supplemetary problems. Page 120
Problem number : 29
Date solved : Monday, January 27, 2025 at 02:27:50 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: 0.003 (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]
 

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