75.8.18 problem 216

Internal problem ID [16834]
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
Date solved : Tuesday, January 28, 2025 at 09:34:21 AM
CAS classification : [_quadrature]

\begin{align*} y^{{2}/{5}}+{y^{\prime }}^{{2}/{5}}&=a^{{2}/{5}} \end{align*}

✓ Solution by Maple

Time used: 0.115 (sec). Leaf size: 26

dsolve(y(x)^(2/5)+diff(y(x),x)^(2/5)=a^(2/5),y(x), singsol=all)
 

\[ x -\int _{}^{y}\frac {1}{\left (-\textit {\_a}^{{2}/{5}}+a^{{2}/{5}}\right )^{{5}/{2}}}d \textit {\_a} -c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.876 (sec). Leaf size: 113

DSolve[y[x]^(2/5)+D[y[x],x]^(2/5)==a^(2/5),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {15 \sqrt [5]{a} \sqrt {1-\frac {\text {$\#$1}^{2/5}}{a^{2/5}}} \left (a^{2/5}-\text {$\#$1}^{2/5}\right ) \arcsin \left (\frac {\sqrt [5]{\text {$\#$1}}}{\sqrt [5]{a}}\right )+20 \text {$\#$1}^{3/5}-15 \sqrt [5]{\text {$\#$1}} a^{2/5}}{3 \left (a^{2/5}-\text {$\#$1}^{2/5}\right )^{3/2}}\&\right ][x+c_1] \\ y(x)\to a \\ \end{align*}