75.1.3 problem 4

Internal problem ID [16666]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 1. Basic concepts and definitions. Exercises page 18
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 09:16:39 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y+3 y^{{1}/{3}} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

dsolve(diff(y(x),x)=y(x)+3*y(x)^(1/3),y(x), singsol=all)
 

\[ y^{{2}/{3}}+3-{\mathrm e}^{\frac {2 x}{3}} c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 1.585 (sec). Leaf size: 39

DSolve[D[y[x],x]==y[x]+3*y[x]^(1/3),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \left (-3+e^{\frac {2 (x+c_1)}{3}}\right ){}^{3/2} \\ y(x)\to 0 \\ y(x)\to -3 i \sqrt {3} \\ \end{align*}