73.5.13 problem 6.7 (a)

Internal problem ID [15124]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.7 (a)
Date solved : Tuesday, January 28, 2025 at 07:34:04 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 56

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

\begin{align*} y &= \left (c_{1} +3 \ln \left (x \right )\right )^{{1}/{3}} x \\ y &= -\frac {\left (c_{1} +3 \ln \left (x \right )\right )^{{1}/{3}} \left (1+i \sqrt {3}\right ) x}{2} \\ y &= \frac {\left (c_{1} +3 \ln \left (x \right )\right )^{{1}/{3}} \left (i \sqrt {3}-1\right ) x}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.176 (sec). Leaf size: 63

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

\begin{align*} y(x)\to x \sqrt [3]{3 \log (x)+c_1} \\ y(x)\to -\sqrt [3]{-1} x \sqrt [3]{3 \log (x)+c_1} \\ y(x)\to (-1)^{2/3} x \sqrt [3]{3 \log (x)+c_1} \\ \end{align*}