Internal problem ID [3088]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 340.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (b \,x^{2}+a \right ) y^{\prime }-c x y \ln \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve((b*x^2+a)*diff(y(x),x) = c*x*y(x)*ln(y(x)),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{{\mathrm e}^{c c_{1}} \left (b \,x^{2}+a \right )^{\frac {c}{2 b}}} \]
✓ Solution by Mathematica
Time used: 0.367 (sec). Leaf size: 33
DSolve[(a+b x^2)y'[x]==c x y[x] Log[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{e^{c_1} \left (a+b x^2\right )^{\frac {c}{2 b}}} \\ y(x)\to 1 \\ \end{align*}