29.12.21 problem 340

Internal problem ID [4940]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 340
Date solved : Monday, January 27, 2025 at 09:53:08 AM
CAS classification : [_separable]

\begin{align*} \left (b \,x^{2}+a \right ) y^{\prime }&=c x y \ln \left (y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 24

dsolve((b*x^2+a)*diff(y(x),x) = c*x*y(x)*ln(y(x)),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{{\mathrm e}^{c c_{1}} \left (b \,x^{2}+a \right )^{\frac {c}{2 b}}} \]

✓ Solution by Mathematica

Time used: 0.348 (sec). Leaf size: 33

DSolve[(a+b x^2)D[y[x],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*}