Internal problem ID [4045]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 28
Problem number: 806.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {{y^{\prime }}^{2}+4 y^{\prime } x^{5}-12 y x^{4}=0} \]
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 23
dsolve(diff(y(x),x)^2+4*x^5*diff(y(x),x)-12*x^4*y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {x^{6}}{3} y \left (x \right ) = c_{1} x^{3}+\frac {3}{4} c_{1}^{2} \end{align*}
✓ Solution by Mathematica
Time used: 2.23 (sec). Leaf size: 217
DSolve[(y'[x])^2+4 x^5 y'[x]-12 x^4 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [\frac {1}{6} \left (\log (y(x))-\frac {x^2 \sqrt {x^6+3 y(x)} \log (y(x))}{\sqrt {x^4 \left (x^6+3 y(x)\right )}}\right )+\frac {x^2 \sqrt {x^6+3 y(x)} \log \left (\sqrt {x^6+3 y(x)}+x^3\right )}{3 \sqrt {x^4 \left (x^6+3 y(x)\right )}}=c_1,y(x)\right ] \text {Solve}\left [\frac {1}{6} \left (\frac {x^2 \sqrt {x^6+3 y(x)} \log (y(x))}{\sqrt {x^4 \left (x^6+3 y(x)\right )}}+\log (y(x))\right )-\frac {x^2 \sqrt {x^6+3 y(x)} \log \left (\sqrt {x^6+3 y(x)}+x^3\right )}{3 \sqrt {x^4 \left (x^6+3 y(x)\right )}}=c_1,y(x)\right ] y(x)\to -\frac {x^6}{3} \end{align*}