7.7.14 problem 14

Internal problem ID [192]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 14
Date solved : Friday, February 07, 2025 at 08:02:47 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} y^{\prime } x^{3}&=y x^{2}-y^{3} \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 28

dsolve(x^3*diff(y(x),x)=x^2*y(x)-y(x)^3,y(x), singsol=all)
 

\begin{align*} y &= \frac {x}{\sqrt {2 \ln \left (x \right )+c_1}} \\ y &= -\frac {x}{\sqrt {2 \ln \left (x \right )+c_1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 6.960 (sec). Leaf size: 86

DSolve[x^2*D[y[x],x]==x^2*y[x]-y[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {i e^x \sqrt {x}}{\sqrt {-4 x \operatorname {ExpIntegralEi}(2 x)+2 e^{2 x}+c_1 (-x)}} \\ y(x)\to \frac {i e^x \sqrt {x}}{\sqrt {-4 x \operatorname {ExpIntegralEi}(2 x)+2 e^{2 x}+c_1 (-x)}} \\ y(x)\to 0 \\ \end{align*}