Internal problem ID [6628]
Book: First order enumerated odes
Section: section 1
Problem number: 65.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\left (a +b x +y c \right )^{6}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 94
dsolve(diff(y(x),x)=(a+b*x+c*y(x))^6,y(x), singsol=all)
\[ y \relax (x ) = \frac {\RootOf \left (\left (\int _{}^{\textit {\_Z}}\frac {1}{c^{7} \textit {\_a}^{6}+6 \textit {\_a}^{5} a \,c^{6}+15 \textit {\_a}^{4} a^{2} c^{5}+20 \textit {\_a}^{3} a^{3} c^{4}+15 \textit {\_a}^{2} a^{4} c^{3}+6 \textit {\_a} \,a^{5} c^{2}+a^{6} c +b}d \textit {\_a} \right ) c -x +c_{1}\right ) c -b x}{c} \]
✓ Solution by Mathematica
Time used: 3.137 (sec). Leaf size: 274
DSolve[y'[x]==(a+b*x+c*y[x])^6,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {-4 \sqrt [6]{b} \text {ArcTan}\left (\frac {\sqrt [6]{c} (a+b x+c y(x))}{\sqrt [6]{b}}\right )+2 \sqrt [6]{b} \text {ArcTan}\left (\sqrt {3}-\frac {2 \sqrt [6]{c} (a+b x+c y(x))}{\sqrt [6]{b}}\right )-2 \sqrt [6]{b} \text {ArcTan}\left (\frac {2 \sqrt [6]{c} (a+b x+c y(x))}{\sqrt [6]{b}}+\sqrt {3}\right )+\sqrt {3} \sqrt [6]{b} \log \left (\sqrt [3]{c} (a+b x+c y(x))^2-\sqrt {3} \sqrt [6]{b} \sqrt [6]{c} (a+b x+c y(x))+\sqrt [3]{b}\right )-\sqrt {3} \sqrt [6]{b} \log \left (\sqrt [3]{c} (a+b x+c y(x))^2+\sqrt {3} \sqrt [6]{b} \sqrt [6]{c} (a+b x+c y(x))+\sqrt [3]{b}\right )+12 a \sqrt [6]{c}+12 b \sqrt [6]{c} x+12 c^{7/6} y(x)}{12 b \sqrt [6]{c}}-\frac {c y(x)}{b}=c_1,y(x)\right ] \]