60.3.178 problem 1182

Internal problem ID [11188]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1182
Date solved : Monday, January 27, 2025 at 10:48:13 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y-5 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

dsolve(x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x)+4*y(x)-5*x=0,y(x), singsol=all)
 

\[ y = x \left (\ln \left (x \right ) x c_{1} +c_{2} x +5\right ) \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 20

DSolve[-5*x + 4*y[x] - 3*x*D[y[x],x] + x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x (c_1 x+2 c_2 x \log (x)+5) \]