57.1.62 problem 62

Internal problem ID [9046]
Book : First order enumerated odes
Section : section 1
Problem number : 62
Date solved : Monday, January 27, 2025 at 05:28:02 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\left (1+6 x +y\right )^{{1}/{4}} \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 107

dsolve(diff(y(x),x)=(1+6*x+y(x))^(1/4),y(x), singsol=all)
 

\[ x -\frac {4 \left (1+6 x +y\right )^{{3}/{4}}}{3}+432 \ln \left (6+\left (1+6 x +y\right )^{{1}/{4}}\right )-432 \ln \left (\left (1+6 x +y\right )^{{1}/{4}}-6\right )+216 \ln \left (6 x +y-1295\right )+12 \sqrt {1+6 x +y}-216 \ln \left (\sqrt {1+6 x +y}+36\right )+216 \ln \left (\sqrt {1+6 x +y}-36\right )-144 \left (1+6 x +y\right )^{{1}/{4}}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.354 (sec). Leaf size: 79

DSolve[D[y[x],x]==(1+6*x+y[x])^(1/4),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {1}{6} \left (y(x)-8 (y(x)+6 x+1)^{3/4}+72 \sqrt {y(x)+6 x+1}-864 \sqrt [4]{y(x)+6 x+1}+5184 \log \left (\sqrt [4]{y(x)+6 x+1}+6\right )+6 x+1\right )-\frac {y(x)}{6}=c_1,y(x)\right ] \]