Internal problem ID [13056]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number: 6.1 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y^{\prime }-\frac {1}{\left (3 x +3 y+2\right )^{2}}=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 24
dsolve(diff(y(x),x)=1/(3*x+3*y(x)+2)^2,y(x), singsol=all)
\[ y = -c_{1} +\frac {\operatorname {RootOf}\left (-\textit {\_Z} +3 c_{1} -3 x -2+\tan \left (\textit {\_Z} \right )\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.162 (sec). Leaf size: 23
DSolve[y'[x]==1/(3*x+3*y[x]+2)^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [y(x)-\frac {1}{3} \arctan (3 y(x)+3 x+2)=c_1,y(x)\right ] \]