60.3.373 problem 1379

Internal problem ID [11383]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1379
Date solved : Monday, January 27, 2025 at 11:18:42 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=\frac {12 y}{\left (1+x \right )^{2} \left (x^{2}+2 x +3\right )} \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 60

dsolve(diff(diff(y(x),x),x) = 12/(x+1)^2/(x^2+2*x+3)*y(x),y(x), singsol=all)
 

\[ y = \frac {3 \left (x^{2}+2 x +3\right ) c_{2} \arctan \left (\frac {\sqrt {2}\, \left (x +1\right )}{2}\right )-c_{2} \left (x^{3}+2 x^{2}+4 x +1\right ) \sqrt {2}+c_{1} \left (x^{2}+2 x +3\right )}{\left (x +1\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 80

DSolve[D[y[x],{x,2}] == (12*y[x])/((1 + x)^2*(3 + 2*x + x^2)),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x-\frac {4}{K[1]^3+3 K[1]^2+5 K[1]+3}dK[1]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[2]}-\frac {4}{K[1]^3+3 K[1]^2+5 K[1]+3}dK[1]\right )dK[2]+c_1\right ) \]