54.3.75 problem 1089

Internal problem ID [12370]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1089
Date solved : Friday, October 03, 2025 at 03:18:45 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} a y^{\prime \prime }-\left (a b +c +x \right ) y^{\prime }+\left (b \left (x +c \right )+d \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 58

ode:=a*diff(diff(y(x),x),x)-(a*b+c+x)*diff(y(x),x)+(b*(x+c)+d)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 63

ode=(d + b*(c + x))*y[x] - (a*b + c + x)*D[y[x],x] + a*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
d = symbols("d") 
y = Function("y") 
ode = Eq(a*Derivative(y(x), (x, 2)) + (b*(c + x) + d)*y(x) - (a*b + c + x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False