29.36.5 problem 1068

Internal problem ID [5632]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 36
Problem number : 1068
Date solved : Monday, January 27, 2025 at 12:40:58 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} 2 x^{3} {y^{\prime }}^{3}+6 x^{2} y {y^{\prime }}^{2}-\left (1-6 y x \right ) y y^{\prime }+2 y^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 3.974 (sec). Leaf size: 2024

dsolve(2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2*y(x)^3 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= 0 \\ \text {Expression too large to display} \\ \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}

✓ Solution by Mathematica

Time used: 62.874 (sec). Leaf size: 179

DSolve[2 x^3 (D[y[x],x])^3 +6 x^2 y[x] (D[y[x],x])^2 -(1-6 x y[x])y[x] D[y[x],x]+2 y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\int _1^x\frac {\text {InverseFunction}\left [-\frac {2 \sqrt {\text {$\#$1}^2-8 \text {$\#$1}^3} \arctan \left (\sqrt {8 \text {$\#$1}-1}\right )}{\text {$\#$1} \sqrt {8 \text {$\#$1}-1}}-14 \log \left (\text {$\#$1}^2 (8 \text {$\#$1}-1)\right )+\log \left (\text {$\#$1}^{14} (8 \text {$\#$1}-1)^{15/2} \left (\text {$\#$1}-\sqrt {\text {$\#$1}^2-8 \text {$\#$1}^3}\right )\right )+\log \left (\text {$\#$1}^{12} (8 \text {$\#$1}-1)^{13/2} \left (\text {$\#$1}+\sqrt {\text {$\#$1}^2-8 \text {$\#$1}^3}\right )\right )+\frac {3 \sqrt {\text {$\#$1}^2-8 \text {$\#$1}^3}}{\text {$\#$1}}\&\right ][c_1+2 \log (K[1])]}{K[1]}dK[1]}{x} \]