10.9.21 problem 27

Internal problem ID [1323]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page 172
Problem number : 27
Date solved : Monday, January 27, 2025 at 04:51:01 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*}

Using reduction of order method given that one solution is

\begin{align*} y&=\sin \left (x^{2}\right ) \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,sin(x^2)],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]
 

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