Internal problem ID [8957]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 622.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], [_Abel, `2nd type`, `class C`]]
\[ \boxed {y^{\prime }-\frac {1}{y+2+\sqrt {3 x +1}}=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 83
dsolve(diff(y(x),x) = 1/(y(x)+2+(3*x+1)^(1/2)),y(x), singsol=all)
\[ \ln \left (3 \sqrt {3 x +1}\, y \left (x \right )+3 y \left (x \right )^{2}+6 \sqrt {3 x +1}-6 x +12 y \left (x \right )+10\right )-\frac {6 \sqrt {3 x +1}\, \operatorname {arctanh}\left (\frac {3 \sqrt {3 x +1}+6 y \left (x \right )+12}{\sqrt {99 x +33}}\right )}{\sqrt {99 x +33}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.233 (sec). Leaf size: 140
DSolve[y'[x] == (2 + Sqrt[1 + 3*x] + y[x])^(-1),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [6 \sqrt {33} \text {arctanh}\left (\frac {3 y(x)+7 \sqrt {3 x+1}+6}{\sqrt {33} \left (y(x)+\sqrt {3 x+1}+2\right )}\right )+44 c_1=33 \left (\log \left (\frac {-3 \sqrt {3 x+1} y(x)^2-3 \left (3 x+4 \sqrt {3 x+1}+1\right ) y(x)+6 x \left (\sqrt {3 x+1}-3\right )-10 \sqrt {3 x+1}-6}{2 (3 x+1)^{3/2}}\right )+\log (12 x+4)\right ),y(x)\right ] \]