54.3.43 problem 1048

Internal problem ID [12338]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1048
Date solved : Friday, October 03, 2025 at 03:18:28 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 x y^{\prime }+\left (3 x^{2}+2 n -1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.032 (sec). Leaf size: 37

ode:=diff(diff(y(x),x),x)-4*x*diff(y(x),x)+(3*x^2+2*n-1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\frac {x^{2}}{2}} x \left (\operatorname {KummerM}\left (\frac {1}{2}-\frac {n}{2}, \frac {3}{2}, x^{2}\right ) c_1 +\operatorname {KummerU}\left (\frac {1}{2}-\frac {n}{2}, \frac {3}{2}, x^{2}\right ) c_2 \right ) \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 37

ode=(-1 + 2*n + 3*x^2)*y[x] - 4*x*D[y[x],x] + D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{\frac {x^2}{2}} \left (c_1 \operatorname {HermiteH}(n,x)+c_2 \operatorname {Hypergeometric1F1}\left (-\frac {n}{2},\frac {1}{2},x^2\right )\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
n = symbols("n") 
y = Function("y") 
ode = Eq(-4*x*Derivative(y(x), x) + (2*n + 3*x**2 - 1)*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False