82.11.3 problem Ex. 3

Internal problem ID [18763]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 28
Problem number : Ex. 3
Date solved : Tuesday, January 28, 2025 at 12:15:31 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} y^{\prime }+\frac {2 y}{x}&=3 x^{2} y^{{1}/{3}} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(diff(y(x),x)+2/x*y(x)=3*x^2*y(x)^(1/3),y(x), singsol=all)
 

\[ y \left (x \right )^{{2}/{3}}-\frac {6 x^{3}}{13}-\frac {c_{1}}{x^{{4}/{3}}} = 0 \]

✓ Solution by Mathematica

Time used: 9.778 (sec). Leaf size: 33

DSolve[D[y[x],x]+2/x*y[x]==3*x^2*y[x]^(1/3),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\left (6 x^3+\frac {13 c_1}{x^{4/3}}\right ){}^{3/2}}{13 \sqrt {13}} \]