Internal problem ID [15126]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 11. Singular solutions of differential equations. Exercises page 92
Problem number: 264.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-y^{\frac {2}{3}}=a} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 85
dsolve(diff(y(x),x)=y(x)^(2/3)+a,y(x), singsol=all)
\[ x -3 y \left (x \right )^{\frac {1}{3}}+2 \sqrt {a}\, \arctan \left (\frac {y \left (x \right )^{\frac {1}{3}}}{\sqrt {a}}\right )-\sqrt {a}\, \arctan \left (\frac {\sqrt {3}\, \sqrt {a}-2 y \left (x \right )^{\frac {1}{3}}}{\sqrt {a}}\right )+\sqrt {a}\, \arctan \left (\frac {2 y \left (x \right )^{\frac {1}{3}}+\sqrt {3}\, \sqrt {a}}{\sqrt {a}}\right )-\sqrt {a}\, \arctan \left (\frac {y \left (x \right )}{a^{\frac {3}{2}}}\right )+c_{1} = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]=y[x]^(2/3)+a,y[x],x,IncludeSingularSolutions -> True]
Not solved