60.1.49 problem 49

Internal problem ID [10063]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 49
Date solved : Monday, January 27, 2025 at 06:20:15 PM
CAS classification : [_Abel]

\begin{align*} y^{\prime }+a \phi ^{\prime }\left (x \right ) y^{3}+6 a \phi \left (x \right ) y^{2}+\frac {\left (2 a +1\right ) y \phi ^{\prime \prime }\left (x \right )}{\phi ^{\prime }\left (x \right )}+2 a +2&=0 \end{align*}

✗ Solution by Maple

dsolve(diff(y(x),x) + a*diff(phi(x),x)*y(x)^3 + 6*a*phi(x)*y(x)^2 +(2*a+1)*y(x)*diff(phi(x),x,x)/diff(phi(x),x) +2*(a+1)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[D[y[x],x] + a*D[ phi[x],x]*y[x]^3 + 6*a*phi[x]*y[x]^2 +(2*a+1)*y[x]*D[ phi[x],x]/D[ phi[x],x] +2*(a+1)==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved