29.36.13 problem 1079

Internal problem ID [5640]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 36
Problem number : 1079
Date solved : Monday, January 27, 2025 at 12:47:32 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.140 (sec). Leaf size: 98

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

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

✓ Solution by Mathematica

Time used: 87.236 (sec). Leaf size: 11250

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

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