60.3.122 problem 1126

Internal problem ID [11132]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1126
Date solved : Monday, January 27, 2025 at 10:46:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(x*diff(y(x),x$2)+(2*a*x^3-1)*diff(y(x),x)+(a^2*x^3+a)*x^2*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {a \,x^{3}}{3}} \left (c_{2} x^{2}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.073 (sec). Leaf size: 34

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

\[ y(x)\to \frac {1}{2} e^{\frac {1}{2}-\frac {a x^3}{3}} \left (c_2 x^2+2 c_1\right ) \]