60.2.46 problem 622

Internal problem ID [10633]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 622
Date solved : Monday, January 27, 2025 at 09:18:54 PM
CAS classification : [[_1st_order, _with_linear_symmetries], [_Abel, `2nd type`, `class C`]]

\begin{align*} y^{\prime }&=\frac {1}{y+2+\sqrt {1+3 x}} \end{align*}

✓ Solution by Maple

Time used: 0.167 (sec). Leaf size: 70

dsolve(diff(y(x),x) = 1/(y(x)+2+(3*x+1)^(1/2)),y(x), singsol=all)
 

\[ -2 \sqrt {33}\, \operatorname {arctanh}\left (\frac {\left (\sqrt {3 x +1}+2 y+4\right ) \sqrt {33}}{11 \sqrt {3 x +1}}\right )+11 \ln \left (\left (3 y+6\right ) \sqrt {3 x +1}+3 y^{2}-6 x +12 y+10\right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.216 (sec). Leaf size: 140

DSolve[D[y[x],x] == (2 + Sqrt[1 + 3*x] + y[x])^(-1),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [6 \sqrt {33} \text {arctanh}\left (\frac {3 y(x)+7 \sqrt {3 x+1}+6}{\sqrt {33} \left (y(x)+\sqrt {3 x+1}+2\right )}\right )+44 c_1=33 \left (\log \left (\frac {-3 \sqrt {3 x+1} y(x)^2-3 \left (3 x+4 \sqrt {3 x+1}+1\right ) y(x)+6 x \left (\sqrt {3 x+1}-3\right )-10 \sqrt {3 x+1}-6}{2 (3 x+1)^{3/2}}\right )+\log (12 x+4)\right ),y(x)\right ] \]