60.3.381 problem 1387

Internal problem ID [11391]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1387
Date solved : Monday, January 27, 2025 at 11:19:08 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }&=\frac {3 y}{4 \left (x^{2}+x +1\right )^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 28

dsolve(diff(diff(y(x),x),x) = 3/4/(x^2+x+1)^2*y(x),y(x), singsol=all)
 

\[ y = \sqrt {x^{2}+x +1}\, \left (\arctan \left (\frac {\left (2 x +1\right ) \sqrt {3}}{3}\right ) c_{2} +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.193 (sec). Leaf size: 39

DSolve[D[y[x],{x,2}] == (3*y[x])/(4*(1 + x + x^2)^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {x^2+x+1} \left (c_2 \int _1^x\frac {1}{K[1]^2+K[1]+1}dK[1]+c_1\right ) \]