29.28.17 problem 815

Internal problem ID [5398]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 28
Problem number : 815
Date solved : Monday, January 27, 2025 at 11:18:53 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-2 \left (1-3 y\right ) y^{\prime }-\left (4-9 y\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.036 (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 \left (x \right ) &= {\frac {4}{9}} \\ y \left (x \right ) &= \frac {\operatorname {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: 60.298 (sec). Leaf size: 4769

DSolve[(D[y[x],x])^2-2*(1-3*y[x])*D[y[x],x]-(4-9*y[x])*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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