Internal problem ID [6078]
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]
\[ \boxed {y^{\prime }-\frac {\left (-1+y+x \right )^{2}}{2 \left (x +2\right )^{2}}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 21
dsolve(diff(y(x),x)=1/2*((x+y(x)-1)/(x+2))^2,y(x), singsol=all)
\[ y \left (x \right ) = 3+\tan \left (\frac {\ln \left (x +2\right )}{2}+\frac {c_{1}}{2}\right ) \left (x +2\right ) \]
✓ Solution by Mathematica
Time used: 0.411 (sec). Leaf size: 99
DSolve[y'[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) \\ y(x)\to i x+(3+2 i) \\ \end{align*}