53.2.9 problem 16

Internal problem ID [8462]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 97. The p-discriminant equation. EXERCISES Page 314
Problem number : 16
Date solved : Monday, January 27, 2025 at 04:02:26 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: 0.137 (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 &= \sqrt {x \left (-i \sqrt {3}-1\right )} \\ y &= \sqrt {\left (i \sqrt {3}-1\right ) x} \\ y &= -\sqrt {-\left (1+i \sqrt {3}\right ) x} \\ y &= -\sqrt {\left (i \sqrt {3}-1\right ) x} \\ y &= \sqrt {x}\, \sqrt {2} \\ y &= -\sqrt {x}\, \sqrt {2} \\ y &= 0 \\ y &= \frac {\left (-c_{1}^{3}+6 c_{1} x \right )^{{1}/{3}} 2^{{2}/{3}}}{2} \\ y &= -\frac {2^{{2}/{3}} \left (-c_{1}^{3}+6 c_{1} x \right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{4} \\ y &= \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: 39.264 (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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