Internal problem ID [9424]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1089.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {a y^{\prime \prime }-\left (a b +c +x \right ) y^{\prime }+\left (b \left (x +c \right )+d \right ) y=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 61
dsolve(a*diff(diff(y(x),x),x)-(a*b+c+x)*diff(y(x),x)+(b*(x+c)+d)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{x b} \operatorname {KummerM}\left (-\frac {d}{2}, \frac {1}{2}, \frac {\left (b a -c -x \right )^{2}}{2 a}\right )+c_{2} {\mathrm e}^{x b} \operatorname {KummerU}\left (-\frac {d}{2}, \frac {1}{2}, \frac {\left (b a -c -x \right )^{2}}{2 a}\right ) \]
✓ Solution by Mathematica
Time used: 0.065 (sec). Leaf size: 63
DSolve[(d + b*(c + x))*y[x] - (a*b + c + x)*y'[x] + a*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{b x} \left (c_1 \operatorname {HermiteH}\left (d,\frac {-a b+c+x}{\sqrt {2} \sqrt {a}}\right )+c_2 \operatorname {Hypergeometric1F1}\left (-\frac {d}{2},\frac {1}{2},\frac {(-a b+c+x)^2}{2 a}\right )\right ) \]