Internal problem ID [6359]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 68.
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 {a y y^{\prime \prime }+b y-c=0} \end {gather*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 68
dsolve(a*y(x)*diff(y(x),x$2)+b*y(x)=c,y(x), singsol=all)
\begin{align*} \int _{}^{y \relax (x )}\frac {a}{\sqrt {a \left (2 c \ln \left (\textit {\_a} \right )+c_{1} a -2 b \textit {\_a} \right )}}d \textit {\_a} -x -c_{2} = 0 \\ \int _{}^{y \relax (x )}-\frac {a}{\sqrt {a \left (2 c \ln \left (\textit {\_a} \right )+c_{1} a -2 b \textit {\_a} \right )}}d \textit {\_a} -x -c_{2} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.617 (sec). Leaf size: 43
DSolve[a*y[x]*y''[x]+b*y[x]==c,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}\frac {1}{\sqrt {c_1+\frac {2 (c \log (K[1])-b K[1])}{a}}}dK[1]{}^2=(x+c_2){}^2,y(x)\right ] \]