Internal problem ID [3799]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 36
Problem number: 1093.
ODE order: 1.
ODE degree: 4.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{4}+4 y \left (y^{\prime }\right )^{3}+6 y^{2} \left (y^{\prime }\right )^{2}-\left (1-4 y^{3}\right ) y^{\prime }-\left (3-y^{3}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.187 (sec). Leaf size: 441
dsolve(diff(y(x),x)^4+4*y(x)*diff(y(x),x)^3+6*y(x)^2*diff(y(x),x)^2-(1-4*y(x)^3)*diff(y(x),x)-(3-y(x)^3)*y(x) = 0,y(x), singsol=all)
\[ x +\frac {\ln \left (-14640 \RootOf \left (\textit {\_Z}^{4}+4 y \relax (x ) \textit {\_Z}^{3}+6 y \relax (x )^{2} \textit {\_Z}^{2}+\left (4 y \relax (x )^{3}-1\right ) \textit {\_Z} +y \relax (x )^{4}-3 y \relax (x )\right )^{3} y \relax (x )^{6}-39648 \RootOf \left (\textit {\_Z}^{4}+4 y \relax (x ) \textit {\_Z}^{3}+6 y \relax (x )^{2} \textit {\_Z}^{2}+\left (4 y \relax (x )^{3}-1\right ) \textit {\_Z} +y \relax (x )^{4}-3 y \relax (x )\right )^{2} y \relax (x )^{7}-36144 \RootOf \left (\textit {\_Z}^{4}+4 y \relax (x ) \textit {\_Z}^{3}+6 y \relax (x )^{2} \textit {\_Z}^{2}+\left (4 y \relax (x )^{3}-1\right ) \textit {\_Z} +y \relax (x )^{4}-3 y \relax (x )\right ) y \relax (x )^{8}-11072 y \relax (x )^{9}-93435 \RootOf \left (\textit {\_Z}^{4}+4 y \relax (x ) \textit {\_Z}^{3}+6 y \relax (x )^{2} \textit {\_Z}^{2}+\left (4 y \relax (x )^{3}-1\right ) \textit {\_Z} +y \relax (x )^{4}-3 y \relax (x )\right )^{3} y \relax (x )^{3}-177915 \RootOf \left (\textit {\_Z}^{4}+4 y \relax (x ) \textit {\_Z}^{3}+6 y \relax (x )^{2} \textit {\_Z}^{2}+\left (4 y \relax (x )^{3}-1\right ) \textit {\_Z} +y \relax (x )^{4}-3 y \relax (x )\right )^{2} y \relax (x )^{4}-162033 \RootOf \left (\textit {\_Z}^{4}+4 y \relax (x ) \textit {\_Z}^{3}+6 y \relax (x )^{2} \textit {\_Z}^{2}+\left (4 y \relax (x )^{3}-1\right ) \textit {\_Z} +y \relax (x )^{4}-3 y \relax (x )\right ) y \relax (x )^{5}-8169 y \relax (x )^{6}-256 \RootOf \left (\textit {\_Z}^{4}+4 y \relax (x ) \textit {\_Z}^{3}+6 y \relax (x )^{2} \textit {\_Z}^{2}+\left (4 y \relax (x )^{3}-1\right ) \textit {\_Z} +y \relax (x )^{4}-3 y \relax (x )\right )^{3}+2048 y \relax (x ) \RootOf \left (\textit {\_Z}^{4}+4 y \relax (x ) \textit {\_Z}^{3}+6 y \relax (x )^{2} \textit {\_Z}^{2}+\left (4 y \relax (x )^{3}-1\right ) \textit {\_Z} +y \relax (x )^{4}-3 y \relax (x )\right )^{2}-9216 y \relax (x )^{2} \RootOf \left (\textit {\_Z}^{4}+4 y \relax (x ) \textit {\_Z}^{3}+6 y \relax (x )^{2} \textit {\_Z}^{2}+\left (4 y \relax (x )^{3}-1\right ) \textit {\_Z} +y \relax (x )^{4}-3 y \relax (x )\right )+124155 y \relax (x )^{3}\right )}{9}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 135.372 (sec). Leaf size: 2925
DSolve[(y'[x])^4 +4 y[x] (y'[x])^3+6 y[x]^2 (y'[x])^2-(1-4 y[x]^3) y'[x]- (3-y[x]^3) y[x]==0,y[x],x,IncludeSingularSolutions -> True]
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