15.2.22 problem 22

Internal problem ID [2892]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 6, page 25
Problem number : 22
Date solved : Monday, January 27, 2025 at 06:27:18 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} y^{2} \left (y y^{\prime }-x \right )+x^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.242 (sec). Leaf size: 56

dsolve(y(x)^2*(y(x)*diff(y(x),x)-x)+x^3=0,y(x), singsol=all)
 

\[ y = \operatorname {RootOf}\left (2 \textit {\_Z}^{2}+\sqrt {3}\, \tan \left (\operatorname {RootOf}\left (-2 \sqrt {3}\, \ln \left (2\right )+\sqrt {3}\, \ln \left (\sec \left (\textit {\_Z} \right )^{2} x^{4}\right )+\sqrt {3}\, \ln \left (3\right )+4 \sqrt {3}\, c_1 -2 \textit {\_Z} \right )\right )-1\right ) x \]

✓ Solution by Mathematica

Time used: 0.118 (sec). Leaf size: 63

DSolve[y[x]^2*(y[x]*D[y[x],x]-x)+x^3==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {\arctan \left (\frac {\frac {2 y(x)^2}{x^2}-1}{\sqrt {3}}\right )}{2 \sqrt {3}}+\frac {1}{4} \log \left (\frac {y(x)^4}{x^4}-\frac {y(x)^2}{x^2}+1\right )=-\log (x)+c_1,y(x)\right ] \]