Internal problem ID [3546]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 28
Problem number: 815.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-2 \left (-3 y+1\right ) y^{\prime }-\left (4-9 y\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 8.141 (sec). Leaf size: 123
dsolve(diff(y(x),x)^2-2*(1-3*y(x))*diff(y(x),x)-(4-9*y(x))*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = {\frac {4}{9}} \\ y \relax (x ) = \frac {\RootOf \left (\textit {\_Z}^{8} {\mathrm e}^{24 x}+24 \textit {\_Z}^{7} {\mathrm e}^{24 x}+240 \textit {\_Z}^{6} {\mathrm e}^{24 x}+1280 \textit {\_Z}^{5} {\mathrm e}^{24 x}+\left (3840 \,{\mathrm e}^{24 x}-1458 \,{\mathrm e}^{12 x} c_{1}\right ) \textit {\_Z}^{4}+\left (6144 \,{\mathrm e}^{24 x}+75816 \,{\mathrm e}^{12 x} c_{1}\right ) \textit {\_Z}^{3}+\left (4096 \,{\mathrm e}^{24 x}-209952 \,{\mathrm e}^{12 x} c_{1}\right ) \textit {\_Z}^{2}-23328 \textit {\_Z} \,{\mathrm e}^{12 x} c_{1}-11664 \,{\mathrm e}^{12 x} c_{1}+531441 c_{1}^{2}\right )}{9}+\frac {4}{9} \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.281 (sec). Leaf size: 4769
DSolve[(y'[x])^2-2(1-3 y[x])y'[x]-(4-9 y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
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