60.3.180 problem 1184

Internal problem ID [11190]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1184
Date solved : Monday, January 27, 2025 at 10:48:17 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y-x^{4}+x^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 25

dsolve(x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+6*y(x)-x^4+x^2=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 30

DSolve[x^2 - x^4 + 6*y[x] - 4*x*D[y[x],x] + x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} x^2 \left (x^2+2 \log (x)+2 c_2 x+2+2 c_1\right ) \]