57.1.63 problem 63

Internal problem ID [9047]
Book : First order enumerated odes
Section : section 1
Problem number : 63
Date solved : Monday, January 27, 2025 at 05:28:04 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\left (a +b x +y\right )^{4} \end{align*}

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 49

dsolve(diff(y(x),x)=(a+b*x+y(x))^(4),y(x), singsol=all)
 

\[ y = -b x +\operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{4}+4 \textit {\_a}^{3} a +6 \textit {\_a}^{2} a^{2}+4 \textit {\_a} \,a^{3}+a^{4}+b}d \textit {\_a} +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.423 (sec). Leaf size: 163

DSolve[D[y[x],x]==(a+b*x+y[x])^(4),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {2 \sqrt {2} \arctan \left (1-\frac {\sqrt {2} (a+b x+y(x))}{\sqrt [4]{b}}\right )-2 \sqrt {2} \arctan \left (\frac {\sqrt {2} (a+b x+y(x))}{\sqrt [4]{b}}+1\right )+\sqrt {2} \log \left ((a+b x+y(x))^2-\sqrt {2} \sqrt [4]{b} (a+b x+y(x))+\sqrt {b}\right )-\sqrt {2} \log \left ((a+b x+y(x))^2+\sqrt {2} \sqrt [4]{b} (a+b x+y(x))+\sqrt {b}\right )+8 b^{3/4} x}{8 b^{3/4}}=c_1,y(x)\right ] \]