Internal problem ID [6358]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 67.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
Solve \begin {gather*} \boxed {3 y y^{\prime \prime }+y-5=0} \end {gather*}
✓ Solution by Maple
Time used: 0.157 (sec). Leaf size: 59
dsolve(3*y(x)*diff(y(x),x$2)+y(x)=5,y(x), singsol=all)
\begin{align*} \int _{}^{y \relax (x )}-\frac {3}{\sqrt {30 \ln \left (\textit {\_a} \right )+9 c_{1}-6 \textit {\_a}}}d \textit {\_a} -x -c_{2} = 0 \\ \int _{}^{y \relax (x )}\frac {3}{\sqrt {30 \ln \left (\textit {\_a} \right )+9 c_{1}-6 \textit {\_a}}}d \textit {\_a} -x -c_{2} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.474 (sec). Leaf size: 41
DSolve[3*y[x]*y''[x]+y[x]==5,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}\frac {1}{\sqrt {c_1+\frac {2}{3} (5 \log (K[1])-K[1])}}dK[1]{}^2=(x+c_2){}^2,y(x)\right ] \]