10.11 problem 15.4

Internal problem ID [13570]

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: 15.4.
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*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 4] \end {align*}

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.0 (sec). Leaf size: 0

DSolve[{x*y''[x]-y'[x]+4*x^3*y[x]==0,{y[0]==1,y'[0]==4}},y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

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