58.2.5 problem 5

Internal problem ID [9128]
Book : Second order enumerated odes
Section : section 2
Problem number : 5
Date solved : Monday, January 27, 2025 at 05:45:49 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} y^{\prime \prime } y^{\prime }+y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.052 (sec). Leaf size: 61

dsolve(diff(y(x),x$2)*diff(y(x),x)+y(x)^2=0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= {\mathrm e}^{\frac {\sqrt {3}\, \left (\int \tan \left (\operatorname {RootOf}\left (-\sqrt {3}\, \ln \left (\cos \left (\textit {\_Z} \right )^{2}\right )-2 \sqrt {3}\, \ln \left (\tan \left (\textit {\_Z} \right )+\sqrt {3}\right )+6 \sqrt {3}\, c_{1} +6 \sqrt {3}\, x +6 \textit {\_Z} \right )\right )d x \right )}{2}+c_{2} +\frac {x}{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.503 (sec). Leaf size: 55

DSolve[D[y[x],{x,2}]*D[y[x],x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 \exp \left (\int _1^x\text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {K[1]}{(K[1]+1) \left (K[1]^2-K[1]+1\right )}dK[1]\&\right ][c_1-K[2]]dK[2]\right ) \]