57.1.61 problem 61

Internal problem ID [9045]
Book : First order enumerated odes
Section : section 1
Problem number : 61
Date solved : Monday, January 27, 2025 at 05:28:00 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\left (1+6 x +y\right )^{{1}/{3}} \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 79

dsolve(diff(y(x),x)=(1+6*x+y(x))^(1/3),y(x), singsol=all)
 

\[ x -\frac {3 \left (1+6 x +y\right )^{{2}/{3}}}{2}+36 \ln \left (\left (1+6 x +y\right )^{{2}/{3}}-6 \left (1+6 x +y\right )^{{1}/{3}}+36\right )-72 \ln \left (6+\left (1+6 x +y\right )^{{1}/{3}}\right )-36 \ln \left (217+6 x +y\right )+18 \left (1+6 x +y\right )^{{1}/{3}}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.241 (sec). Leaf size: 66

DSolve[D[y[x],x]==(1+6*x+y[x])^(1/3),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {1}{6} \left (y(x)-9 (y(x)+6 x+1)^{2/3}+108 \sqrt [3]{y(x)+6 x+1}-648 \log \left (\sqrt [3]{y(x)+6 x+1}+6\right )+6 x+1\right )-\frac {y(x)}{6}=c_1,y(x)\right ] \]