60.3.393 problem 1399

Internal problem ID [11403]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1399
Date solved : Monday, January 27, 2025 at 11:19:30 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=\frac {\left (1+3 x \right ) y^{\prime }}{\left (x -1\right ) \left (1+x \right )}-\frac {36 \left (1+x \right )^{2} y}{\left (x -1\right )^{2} \left (3 x +5\right )^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 34

dsolve(diff(diff(y(x),x),x) = 1/(x-1)*(3*x+1)/(x+1)*diff(y(x),x)-36*(x+1)^2/(x-1)^2/(3*x+5)^2*y(x),y(x), singsol=all)
 

\[ y = \left (x -1\right )^{{3}/{2}} \sqrt {3 x +5}\, \left (3 \ln \left (x -1\right ) c_{2} +\ln \left (3 x +5\right ) c_{2} +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 2.341 (sec). Leaf size: 137

DSolve[D[y[x],{x,2}] == (-36*(1 + x)^2*y[x])/((-1 + x)^2*(5 + 3*x)^2) + ((1 + 3*x)*D[y[x],x])/((-1 + x)*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x\frac {3 K[1] (K[1]+2)+7}{2 (K[1]-1) (K[1]+1) (3 K[1]+5)}dK[1]-\frac {1}{2} \int _1^x\frac {3 K[2]+1}{1-K[2]^2}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {3 K[1] (K[1]+2)+7}{2 (K[1]-1) (K[1]+1) (3 K[1]+5)}dK[1]\right )dK[3]+c_1\right ) \]