Internal problem ID [13954]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 34. Power series solutions II: Generalization and theory. Additional Exercises.
page 678
Problem number: 34.5 (j).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\sin \left (\pi \,x^{2}\right ) y^{\prime \prime }+x^{2} y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 46
Order:=6; dsolve(sin(Pi*x^2)*diff(y(x),x$2)+x^2*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-\frac {x^{2}}{2 \pi }+\frac {x^{4}}{24 \pi ^{2}}\right ) y \left (0\right )+\left (x -\frac {x^{3}}{6 \pi }+\frac {x^{5}}{120 \pi ^{2}}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 54
AsymptoticDSolveValue[Sin[Pi*x^2]*y''[x]+x^2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^5}{120 \pi ^2}-\frac {x^3}{6 \pi }+x\right )+c_1 \left (\frac {x^4}{24 \pi ^2}-\frac {x^2}{2 \pi }+1\right ) \]