Internal problem ID [6626]
Book: First order enumerated odes
Section: section 1
Problem number: 63.
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\right )^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 49
dsolve(diff(y(x),x)=(a+b*x+y(x))^(4),y(x), singsol=all)
\[ y \relax (x ) = -b x +\RootOf \left (-x +\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{4}+4 \textit {\_a}^{3} a +6 \textit {\_a}^{2} a^{2}+4 \textit {\_a} \,a^{3}+a^{4}+b}d \textit {\_a} +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.747 (sec). Leaf size: 163
DSolve[y'[x]==(a+b*x+y[x])^(4),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2 \sqrt {2} \text {ArcTan}\left (1-\frac {\sqrt {2} (a+b x+y(x))}{\sqrt [4]{b}}\right )-2 \sqrt {2} \text {ArcTan}\left (\frac {\sqrt {2} (a+b x+y(x))}{\sqrt [4]{b}}+1\right )+\sqrt {2} \log \left ((a+b x+y(x))^2-\sqrt {2} \sqrt [4]{b} (a+b x+y(x))+\sqrt {b}\right )-\sqrt {2} \log \left ((a+b x+y(x))^2+\sqrt {2} \sqrt [4]{b} (a+b x+y(x))+\sqrt {b}\right )+8 b^{3/4} x}{8 b^{3/4}}=c_1,y(x)\right ] \]