Internal problem ID [5325]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\left (x +y-1\right )^{2}}{2 \left (x +2\right )^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 21
dsolve(diff(y(x),x)=1/2*((x+y(x)-1)/(x+2))^2,y(x), singsol=all)
\[ y \relax (x ) = 3+\tan \left (\frac {\ln \left (x +2\right )}{2}+\frac {c_{1}}{2}\right ) \left (x +2\right ) \]
✓ Solution by Mathematica
Time used: 0.598 (sec). Leaf size: 57
DSolve[y'[x]==1/2*((x+y[x]-1)/(x+2))^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -i (x+(2+3 i))-\frac {4 c_1 (x+2)}{2^i (x+2)^i+2 i c_1} \\ y(x)\to i x+(3+2 i) \\ \end{align*}