73.7.18 problem 18

Internal problem ID [15176]
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 : 18
Date solved : Tuesday, January 28, 2025 at 07:40:06 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

\begin{align*} y^{\prime }&=\frac {3 y}{1+x}-y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 34

dsolve(diff(y(x),x)=3*y(x)/(1+x)-y(x)^2,y(x), singsol=all)
 

\[ y = \frac {4 \left (x +1\right )^{3}}{x^{4}+4 x^{3}+6 x^{2}+4 c_{1} +4 x +1} \]

✓ Solution by Mathematica

Time used: 0.202 (sec). Leaf size: 41

DSolve[D[y[x],x]==3*y[x]/(1+x)-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {4 (x+1)^3}{x^4+4 x^3+6 x^2+4 x+1+4 c_1} \\ y(x)\to 0 \\ \end{align*}