60.3.119 problem 1123

Internal problem ID [11129]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1123
Date solved : Monday, January 27, 2025 at 10:46:28 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 45

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

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

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 53

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

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