53.4.21 problem 23

Internal problem ID [8509]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing. EXERCISES Page 324
Problem number : 23
Date solved : Monday, January 27, 2025 at 04:08:36 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 21

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

\[ y(x)\to \frac {c_1 x^2}{2}+x+\frac {1}{x}+c_2 \]