29.36.17 problem 1085

Internal problem ID [5644]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 36
Problem number : 1085
Date solved : Monday, January 27, 2025 at 12:59:25 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.266 (sec). Leaf size: 161

dsolve(y(x)^4*diff(y(x),x)^3-6*x*diff(y(x),x)+2*y(x) = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \sqrt {x \left (-1-i \sqrt {3}\right )} \\ y \left (x \right ) &= \sqrt {\left (i \sqrt {3}-1\right ) x} \\ y \left (x \right ) &= -\sqrt {-\left (1+i \sqrt {3}\right ) x} \\ y \left (x \right ) &= -\sqrt {\left (i \sqrt {3}-1\right ) x} \\ y \left (x \right ) &= \sqrt {2}\, \sqrt {x} \\ y \left (x \right ) &= -\sqrt {2}\, \sqrt {x} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {2^{{2}/{3}} \left (-c_{1}^{3}+6 c_{1} x \right )^{{1}/{3}}}{2} \\ y \left (x \right ) &= -\frac {2^{{2}/{3}} \left (-c_{1}^{3}+6 c_{1} x \right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{4} \\ y \left (x \right ) &= \frac {2^{{2}/{3}} \left (-c_{1}^{3}+6 c_{1} x \right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 69.570 (sec). Leaf size: 22649

DSolve[y[x]^4 (D[y[x],x])^3 -6 x D[y[x],x] +2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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