60.3.295 problem 1301

Internal problem ID [11305]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1301
Date solved : Monday, January 27, 2025 at 11:10:55 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

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

\[ y = \frac {c_{1} +c_{2} \left (a x +b \right )^{3}}{x} \]

✓ Solution by Mathematica

Time used: 0.277 (sec). Leaf size: 87

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

\[ y(x)\to \frac {\left (a^3 c_2 x^3+3 a^2 b c_2 x^2+3 a \left (b^2 c_2 x+c_1\right )+b^3 c_2\right ) \exp \left (-\frac {1}{2} \int _1^x\frac {2 b}{K[1] (b+a K[1])}dK[1]\right )}{3 a (a x+b)} \]