49.23.6 problem 1(f)

Internal problem ID [7764]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 6. Existence and uniqueness of solutions to systems and nth order equations. Page 238
Problem number : 1(f)
Date solved : Monday, January 27, 2025 at 03:12:16 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }-2 y^{\prime }&=x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(x*diff(y(x),x$2)-2*diff(y(x),x)=x^3,y(x), singsol=all)
 

\[ y = \frac {1}{4} x^{4}+\frac {1}{3} c_{1} x^{3}+c_{2} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 24

DSolve[x*D[y[x],{x,2}]-2*D[y[x],x]==x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^4}{4}+\frac {c_1 x^3}{3}+c_2 \]