Internal problem ID [13567]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {x y^{\prime \prime }-y^{\prime }+4 y x^{3}=0} \] With initial conditions \begin {align*} \left [y \left (\sqrt {\pi }\right ) = 3, y^{\prime }\left (\sqrt {\pi }\right ) = 4\right ] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 20
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)
\[ y \left (x \right ) = \frac {-3 \cos \left (x^{2}\right ) \sqrt {\pi }-2 \sin \left (x^{2}\right )}{\sqrt {\pi }} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 23
DSolve[{x*y''[x]-y'[x]+4*x^3*y[x]==0,{y[Sqrt[Pi]]==3,y'[Sqrt[Pi]]==4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {2 \sin \left (x^2\right )}{\sqrt {\pi }}-3 \cos \left (x^2\right ) \]