60.3.137 problem 1141

Internal problem ID [11147]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1141
Date solved : Monday, January 27, 2025 at 10:46:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 55

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

\[ y = \frac {{\mathrm e}^{-\frac {b x}{a}} \operatorname {Ei}_{1}\left (-\frac {b x}{a}\right ) c_{2} b^{2} x^{2}+c_{1} {\mathrm e}^{-\frac {b x}{a}} x^{2}+a c_{2} \left (b x +a \right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.470 (sec). Leaf size: 42

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

\[ y(x)\to e^{-\frac {b x}{a}} \left (c_2 \int _1^x\frac {e^{\frac {b K[1]}{a}}}{K[1]^3}dK[1]+c_1\right ) \]