Internal problem ID [2332]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 37, page 171
Problem number: 19.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y {y^{\prime }}^{2}-3 x y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 1.922 (sec). Leaf size: 273
dsolve(diff(y(x),x)^2*y(x)=3*diff(y(x),x)*x+y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ \ln \left (x \right )-\frac {3 \,\operatorname {arctanh}\left (\frac {3}{\sqrt {\frac {9 x^{2}+4 y \left (x \right )^{2}}{x^{2}}}}\right )}{8}+\frac {5 \,\operatorname {arctanh}\left (\frac {9 x +8 y \left (x \right )}{5 x \sqrt {\frac {9 x^{2}+4 y \left (x \right )^{2}}{x^{2}}}}\right )}{16}-\frac {5 \,\operatorname {arctanh}\left (\frac {-9 x +8 y \left (x \right )}{5 x \sqrt {\frac {9 x^{2}+4 y \left (x \right )^{2}}{x^{2}}}}\right )}{16}+\frac {5 \ln \left (\frac {y \left (x \right )+2 x}{x}\right )}{16}+\frac {5 \ln \left (\frac {-2 x +y \left (x \right )}{x}\right )}{16}+\frac {3 \ln \left (\frac {y \left (x \right )}{x}\right )}{8}-c_{1} &= 0 \\ \ln \left (x \right )+\frac {3 \,\operatorname {arctanh}\left (\frac {3}{\sqrt {\frac {9 x^{2}+4 y \left (x \right )^{2}}{x^{2}}}}\right )}{8}-\frac {5 \,\operatorname {arctanh}\left (\frac {9 x +8 y \left (x \right )}{5 x \sqrt {\frac {9 x^{2}+4 y \left (x \right )^{2}}{x^{2}}}}\right )}{16}+\frac {5 \,\operatorname {arctanh}\left (\frac {-9 x +8 y \left (x \right )}{5 x \sqrt {\frac {9 x^{2}+4 y \left (x \right )^{2}}{x^{2}}}}\right )}{16}+\frac {5 \ln \left (\frac {y \left (x \right )+2 x}{x}\right )}{16}+\frac {5 \ln \left (\frac {-2 x +y \left (x \right )}{x}\right )}{16}+\frac {3 \ln \left (\frac {y \left (x \right )}{x}\right )}{8}-c_{1} &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 75.255 (sec). Leaf size: 2113
DSolve[y'[x]^2*y[x]==3*y'[x]*x+y[x],y[x],x,IncludeSingularSolutions -> True]
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