73.10.8 problem 15.2 (h)

Internal problem ID [15303]
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 : 15.2 (h)
Date solved : Tuesday, January 28, 2025 at 07:51:58 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*}

With initial conditions

\begin{align*} y \left (\sqrt {\pi }\right )&=3\\ y^{\prime }\left (\sqrt {\pi }\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.086 (sec). Leaf size: 24

dsolve([x*diff(y(x),x$2)-diff(y(x),x)+4*x^3*y(x)=0,y(Pi^(1/2)) = 3, D(y)(Pi^(1/2)) = 4],y(x), singsol=all)
 

\[ y = \frac {-3 \cos \left (x^{2}\right ) \sqrt {\pi }-2 \sin \left (x^{2}\right )}{\sqrt {\pi }} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 23

DSolve[{x*D[y[x],{x,2}]-D[y[x],x]+4*x^3*y[x]==0,{y[Sqrt[Pi]]==3,Derivative[1][y][Sqrt[Pi]]==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {2 \sin \left (x^2\right )}{\sqrt {\pi }}-3 \cos \left (x^2\right ) \]