Internal problem ID [15104]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 8. First order not solved for the derivative. Exercises page 67
Problem number: 216.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\frac {2}{5}}+{y^{\prime }}^{\frac {2}{5}}=a^{\frac {2}{5}}} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 26
dsolve(y(x)^(2/5)+diff(y(x),x)^(2/5)=a^(2/5),y(x), singsol=all)
\[ x -\left (\int _{}^{y \left (x \right )}\frac {1}{\left (a^{\frac {2}{5}}-\textit {\_a}^{\frac {2}{5}}\right )^{\frac {5}{2}}}d \textit {\_a} \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.746 (sec). Leaf size: 89
DSolve[y[x]^(2/5)+y'[x]^(2/5)==a^(2/5),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [5 \arctan \left (\frac {\sqrt [5]{\text {$\#$1}}}{\sqrt {a^{2/5}-\text {$\#$1}^{2/5}}}\right )+\frac {5 \sqrt [5]{\text {$\#$1}} \left (4 \text {$\#$1}^{2/5}-3 a^{2/5}\right )}{3 \left (a^{2/5}-\text {$\#$1}^{2/5}\right )^{3/2}}\&\right ][x+c_1] \\ y(x)\to a \\ \end{align*}