60.3.57 problem 1058

Internal problem ID [11067]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1058
Date solved : Monday, January 27, 2025 at 10:43:36 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-x^{2} \left (1+x \right ) y^{\prime }+x \left (x^{4}-2\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 6.645 (sec). Leaf size: 29

dsolve(diff(diff(y(x),x),x)-x^2*(x+1)*diff(y(x),x)+x*(x^4-2)*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{\frac {x^{3}}{3}} \left (c_{1} +\left (\int {\mathrm e}^{\frac {1}{4} x^{4}-\frac {1}{3} x^{3}}d x \right ) c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.446 (sec). Leaf size: 44

DSolve[x*(-2 + x^4)*y[x] - x^2*(1 + x)*D[y[x],x] + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{\frac {x^3}{3}} \left (c_2 \int _1^xe^{\frac {1}{12} K[1]^3 (3 K[1]-4)}dK[1]+c_1\right ) \]