Internal problem ID [6624]
Book: First order enumerated odes
Section: section 1
Problem number: 61.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\left (1+6 x +y\right )^{\frac {1}{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 79
dsolve(diff(y(x),x)=(1+6*x+y(x))^(1/3),y(x), singsol=all)
\[ x -\frac {3 \left (1+6 x +y \relax (x )\right )^{\frac {2}{3}}}{2}+36 \ln \left (\left (1+6 x +y \relax (x )\right )^{\frac {2}{3}}-6 \left (1+6 x +y \relax (x )\right )^{\frac {1}{3}}+36\right )-72 \ln \left (6+\left (1+6 x +y \relax (x )\right )^{\frac {1}{3}}\right )-36 \ln \left (217+6 x +y \relax (x )\right )+18 \left (1+6 x +y \relax (x )\right )^{\frac {1}{3}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.47 (sec). Leaf size: 66
DSolve[y'[x]==(1+6*x+y[x])^(1/3),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{6} \left (y(x)-9 (y(x)+6 x+1)^{2/3}+108 \sqrt [3]{y(x)+6 x+1}-648 \log \left (\sqrt [3]{y(x)+6 x+1}+6\right )+6 x+1\right )-\frac {y(x)}{6}=c_1,y(x)\right ] \]