Internal problem ID [3486]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 753.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+3 x^{2}-8 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 153
dsolve(diff(y(x),x)^2+3*x^2 = 8*y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {3 x^{2}}{8}+\frac {\RootOf \left (\textit {\_Z}^{6}-18 x \,\textit {\_Z}^{5}+135 x^{2} \textit {\_Z}^{4}-540 x^{3} \textit {\_Z}^{3}+\left (1215 x^{4}-16 c_{1}\right ) \textit {\_Z}^{2}+\left (-1458 x^{5}+32 c_{1} x \right ) \textit {\_Z} +729 x^{6}-16 c_{1} x^{2}\right )^{2}}{8} \\ y \relax (x ) = \frac {3 x^{2}}{8}+\frac {\RootOf \left (\textit {\_Z}^{6}+18 x \,\textit {\_Z}^{5}+135 x^{2} \textit {\_Z}^{4}+540 x^{3} \textit {\_Z}^{3}+\left (1215 x^{4}-16 c_{1}\right ) \textit {\_Z}^{2}+\left (1458 x^{5}-32 c_{1} x \right ) \textit {\_Z} +729 x^{6}-16 c_{1} x^{2}\right )^{2}}{8} \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.848 (sec). Leaf size: 2467
DSolve[(y'[x])^2+3 x^2==8 y[x],y[x],x,IncludeSingularSolutions -> True]
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