73.7.32 problem 32

Internal problem ID [15190]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 32
Date solved : Tuesday, January 28, 2025 at 07:41:25 AM
CAS classification : [_quadrature]

\begin{align*} \left (x +2\right ) y^{\prime }-x^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 25

dsolve((x+2)*diff(y(x),x)-x^3=0,y(x), singsol=all)
 

\[ y = \frac {x^{3}}{3}-x^{2}+4 x -8 \ln \left (x +2\right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 26

DSolve[(x+2)*D[y[x],x]-x^3==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\frac {K[1]^3}{K[1]+2}dK[1]+c_1 \]