Internal problem ID [7378]
Book: First order enumerated odes
Section: section 1
Problem number: 62.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y^{\prime }-\left (1+6 x +y\right )^{\frac {1}{4}}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 109
dsolve(diff(y(x),x)=(1+6*x+y(x))^(1/4),y(x), singsol=all)
\[ x +216 \ln \left (-y \left (x \right )-6 x +1295\right )+12 \sqrt {1+6 x +y \left (x \right )}+216 \ln \left (\sqrt {1+6 x +y \left (x \right )}-36\right )-216 \ln \left (\sqrt {1+6 x +y \left (x \right )}+36\right )-144 \left (1+6 x +y \left (x \right )\right )^{\frac {1}{4}}+432 \ln \left (6+\left (1+6 x +y \left (x \right )\right )^{\frac {1}{4}}\right )-432 \ln \left (\left (1+6 x +y \left (x \right )\right )^{\frac {1}{4}}-6\right )-\frac {4 \left (1+6 x +y \left (x \right )\right )^{\frac {3}{4}}}{3}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 2.535 (sec). Leaf size: 79
DSolve[y'[x]==(1+6*x+y[x])^(1/4),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{6} \left (y(x)-8 (y(x)+6 x+1)^{3/4}+72 \sqrt {y(x)+6 x+1}-864 \sqrt [4]{y(x)+6 x+1}+5184 \log \left (\sqrt [4]{y(x)+6 x+1}+6\right )+6 x+1\right )-\frac {y(x)}{6}=c_1,y(x)\right ] \]