10.2.2 problem 2

Internal problem ID [1130]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 2
Date solved : Monday, January 27, 2025 at 04:35:04 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {x^{2}}{\left (x^{3}+1\right ) y} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 39

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

\begin{align*} y &= -\frac {\sqrt {6 \ln \left (x^{3}+1\right )+9 c_1}}{3} \\ y &= \frac {\sqrt {6 \ln \left (x^{3}+1\right )+9 c_1}}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.092 (sec). Leaf size: 56

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

\begin{align*} y(x)\to -\sqrt {\frac {2}{3}} \sqrt {\log \left (x^3+1\right )+3 c_1} \\ y(x)\to \sqrt {\frac {2}{3}} \sqrt {\log \left (x^3+1\right )+3 c_1} \\ \end{align*}