29.36.25 problem 1094

Internal problem ID [5652]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 36
Problem number : 1094
Date solved : Monday, January 27, 2025 at 01:01:30 PM
CAS classification : [_quadrature]

\begin{align*} 2 {y^{\prime }}^{4}-y^{\prime } y-2&=0 \end{align*}

✓ Solution by Maple

Time used: 0.076 (sec). Leaf size: 217

dsolve(2*diff(y(x),x)^4-y(x)*diff(y(x),x)-2 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {\sqrt {-6 \sqrt {\left (c_{1}^{2}-2 c_{1} x +x^{2}+12\right )^{3}}-6 c_{1}^{3}+18 c_{1}^{2} x +\left (-18 x^{2}+216\right ) c_{1} +6 x^{3}-216 x}}{9} \\ y \left (x \right ) &= \frac {\sqrt {-6 \sqrt {\left (c_{1}^{2}-2 c_{1} x +x^{2}+12\right )^{3}}-6 c_{1}^{3}+18 c_{1}^{2} x +\left (-18 x^{2}+216\right ) c_{1} +6 x^{3}-216 x}}{9} \\ y \left (x \right ) &= -\frac {\sqrt {6 \sqrt {\left (c_{1}^{2}-2 c_{1} x +x^{2}+12\right )^{3}}-6 c_{1}^{3}+18 c_{1}^{2} x +\left (-18 x^{2}+216\right ) c_{1} +6 x^{3}-216 x}}{9} \\ y \left (x \right ) &= \frac {\sqrt {6 \sqrt {\left (c_{1}^{2}-2 c_{1} x +x^{2}+12\right )^{3}}-6 c_{1}^{3}+18 c_{1}^{2} x +\left (-18 x^{2}+216\right ) c_{1} +6 x^{3}-216 x}}{9} \\ \end{align*}

✓ Solution by Mathematica

Time used: 113.923 (sec). Leaf size: 12753

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

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