Internal problem ID [5326]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 9. Equations of first order and higher degree. Supplemetary problems. Page
65
Problem number: 20.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {3 x^{4} {y^{\prime }}^{2}-y^{\prime } x -y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 147
dsolve(3*x^4*diff(y(x),x)^2-x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\begin{align*} y = -\frac {1}{12 x^{2}} y = \frac {-c_{1}^{2}-c_{1} \left (-c_{1} +2 i x \sqrt {3}\right )-6 x^{2}}{6 c_{1}^{2} x^{2}} y = \frac {-c_{1}^{2}-c_{1} \left (-c_{1} -2 i x \sqrt {3}\right )-6 x^{2}}{6 c_{1}^{2} x^{2}} y = \frac {c_{1} \left (c_{1} +2 i x \sqrt {3}\right )-6 x^{2}-c_{1}^{2}}{6 c_{1}^{2} x^{2}} y = \frac {c_{1} \left (c_{1} -2 i x \sqrt {3}\right )-6 x^{2}-c_{1}^{2}}{6 c_{1}^{2} x^{2}} \end{align*}
✓ Solution by Mathematica
Time used: 0.512 (sec). Leaf size: 123
DSolve[3*x^4*y'[x]^2-x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [-\frac {x \sqrt {12 x^2 y(x)+1} \text {arctanh}\left (\sqrt {12 x^2 y(x)+1}\right )}{\sqrt {12 x^4 y(x)+x^2}}-\frac {1}{2} \log (y(x))=c_1,y(x)\right ] \text {Solve}\left [\frac {x \sqrt {12 x^2 y(x)+1} \text {arctanh}\left (\sqrt {12 x^2 y(x)+1}\right )}{\sqrt {12 x^4 y(x)+x^2}}-\frac {1}{2} \log (y(x))=c_1,y(x)\right ] y(x)\to 0 \end{align*}