13.9 problem 29

Internal problem ID [5420]

Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section: Chapter 18. Linear equations with variable coefficients (Equations of second order). Supplemetary problems. Page 120
Problem number: 29.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\[ \boxed {x y^{\prime \prime }-y^{\prime }+4 y x^{3}=0} \]

Solution by Maple

Time used: 0.0 (sec). Leaf size: 17

dsolve(x*diff(y(x),x$2)-diff(y(x),x)+4*x^3*y(x)=0,y(x), 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*y''[x]-y'[x]+4*x^3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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