60.3.85 problem 1089

Internal problem ID [11095]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1089
Date solved : Tuesday, January 28, 2025 at 05:41:06 PM
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*}

✓ Solution by Maple

Time used: 0.061 (sec). Leaf size: 58

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)
 

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

✓ Solution by Mathematica

Time used: 0.064 (sec). Leaf size: 63

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

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