15.7.13 problem 13

Internal problem ID [2994]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 11, page 45
Problem number : 13
Date solved : Monday, January 27, 2025 at 07:06:06 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }+2 y&=3 x^{3} y^{{4}/{3}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(x*diff(y(x),x)+2*y(x)=3*x^3*y(x)^(4/3),y(x), singsol=all)
 

\[ \frac {1}{y^{{1}/{3}}}+\frac {3 x^{3}}{7}-x^{{2}/{3}} c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.185 (sec). Leaf size: 29

DSolve[x*D[y[x],x]+2*y[x]==3*x^3*y[x]^(4/3),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {343}{x^2 \left (3 x^{7/3}-7 c_1\right ){}^3} \\ y(x)\to 0 \\ \end{align*}