49.21.16 problem 6(b)

Internal problem ID [7746]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 190
Problem number : 6(b)
Date solved : Monday, January 27, 2025 at 03:11:57 PM
CAS classification : [[_homogeneous, `class C`], _rational, _Riccati]

\begin{align*} y^{\prime }&=\frac {\left (x +y-1\right )^{2}}{2 \left (x +2\right )^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 21

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

\[ y = 3+\tan \left (\frac {\ln \left (x +2\right )}{2}+\frac {c_{1}}{2}\right ) \left (x +2\right ) \]

✓ Solution by Mathematica

Time used: 0.569 (sec). Leaf size: 86

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

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