60.3.71 problem 1072

Internal problem ID [11081]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1072
Date solved : Monday, January 27, 2025 at 10:44:32 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+a p^{\prime \prime }\left (x \right ) y^{\prime }+\left (a +b p \left (x \right )-4 n a p \left (x \right )^{2}\right ) y&=0 \end{align*}

✗ Solution by Maple

dsolve(diff(diff(y(x),x),x)+a*diff(diff(p(x),x),x)*diff(y(x),x)+(a+b*p(x)-4*n*a*p(x)^2)*y(x)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[(a + b*p[x] - 4*a*n*p[x]^2)*y[x] + a*D[y[x],x]*Derivative[2][p][x] + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved