Internal problem ID [4171]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 32
Problem number: 937.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {3 x^{4} {y^{\prime }}^{2}-y x -y=0} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 201
dsolve(3*x^4*diff(y(x),x)^2-x*y(x)-y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\left (\sqrt {3}\, \operatorname {arctanh}\left (\sqrt {x +1}\right ) x \sqrt {x +1}+3 c_{1} x \sqrt {x +1}+\sqrt {3}\, x +\sqrt {3}\right )^{2}}{36 \left (x +1\right ) x^{2}} \\ y \left (x \right ) &= \frac {\left (\sqrt {3}\, \operatorname {arctanh}\left (\sqrt {x +1}\right ) x \sqrt {x +1}-3 c_{1} x \sqrt {x +1}+\sqrt {3}\, x +\sqrt {3}\right )^{2}}{36 \left (x +1\right ) x^{2}} \\ y \left (x \right ) &= \frac {\left (\sqrt {3}\, \operatorname {arctanh}\left (\sqrt {x +1}\right ) x \sqrt {x +1}-3 c_{1} x \sqrt {x +1}+\sqrt {3}\, x +\sqrt {3}\right )^{2}}{36 \left (x +1\right ) x^{2}} \\ y \left (x \right ) &= \frac {\left (\sqrt {3}\, \operatorname {arctanh}\left (\sqrt {x +1}\right ) x \sqrt {x +1}+3 c_{1} x \sqrt {x +1}+\sqrt {3}\, x +\sqrt {3}\right )^{2}}{36 \left (x +1\right ) x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.153 (sec). Leaf size: 171
DSolve[3 x^4 (y'[x])^2-x y[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2 \text {arctanh}\left (\sqrt {x+1}\right )^2+2 x \text {arctanh}\left (\sqrt {x+1}\right ) \left (\sqrt {x+1}-\sqrt {3} c_1 x\right )+3 c_1{}^2 x^2+x-2 \sqrt {3} c_1 x \sqrt {x+1}+1}{12 x^2} \\ y(x)\to \frac {x^2 \text {arctanh}\left (\sqrt {x+1}\right )^2+2 x \text {arctanh}\left (\sqrt {x+1}\right ) \left (\sqrt {x+1}+\sqrt {3} c_1 x\right )+3 c_1{}^2 x^2+x+2 \sqrt {3} c_1 x \sqrt {x+1}+1}{12 x^2} \\ y(x)\to 0 \\ \end{align*}