29.36.26 problem 1095

Internal problem ID [5653]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 36
Problem number : 1095
Date solved : Monday, January 27, 2025 at 01:01:31 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} x {y^{\prime }}^{4}-2 y {y^{\prime }}^{3}+12 x^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.167 (sec). Leaf size: 66

dsolve(x*diff(y(x),x)^4-2*y(x)*diff(y(x),x)^3+12*x^3 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {2 \sqrt {6}\, \left (-x \right )^{{3}/{2}}}{3} \\ y \left (x \right ) &= -\frac {2 \sqrt {6}\, \left (-x \right )^{{3}/{2}}}{3} \\ y \left (x \right ) &= -\frac {2 \sqrt {6}\, x^{{3}/{2}}}{3} \\ y \left (x \right ) &= \frac {2 \sqrt {6}\, x^{{3}/{2}}}{3} \\ y \left (x \right ) &= \frac {12 c_{1}^{4}+x^{2}}{2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 70.298 (sec). Leaf size: 30947

DSolve[x (D[y[x],x])^4 -2 y[x] (D[y[x],x])^3+12 x^3==0,y[x],x,IncludeSingularSolutions -> True]
 

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