60.3.140 problem 1144

Internal problem ID [11150]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1144
Date solved : Tuesday, January 28, 2025 at 05:41:33 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.196 (sec). Leaf size: 153

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

\[ y = \frac {{\mathrm e}^{-\frac {b x}{2 a}} \left (-\left (a \left (4 c +b \right )-x \,b^{2}\right ) c c_{1} \operatorname {KummerM}\left (\frac {b -2 c}{2 b}, \frac {3}{2}, \frac {b x}{2 a}\right )+\left (a \left (4 c +b \right )-x \,b^{2}\right ) b c_{2} \operatorname {KummerU}\left (\frac {b -2 c}{2 b}, \frac {3}{2}, \frac {b x}{2 a}\right )+2 a \left (c c_{1} \left (c +b \right ) \operatorname {KummerM}\left (-\frac {b +2 c}{2 b}, \frac {3}{2}, \frac {b x}{2 a}\right )+\operatorname {KummerU}\left (-\frac {b +2 c}{2 b}, \frac {3}{2}, \frac {b x}{2 a}\right ) b^{2} c_{2} \right )\right )}{a \left (b -2 c \right ) c} \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 69

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

\[ y(x)\to e^{-\frac {b x}{2 a}} \left (c_1 \operatorname {HypergeometricU}\left (\frac {3}{2}-\frac {c}{b},\frac {3}{2},\frac {b x}{2 a}\right )+c_2 L_{\frac {c}{b}-\frac {3}{2}}^{\frac {1}{2}}\left (\frac {b x}{2 a}\right )\right ) \]