60.3.326 problem 1332

Internal problem ID [11336]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1332
Date solved : Monday, January 27, 2025 at 11:15:27 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.317 (sec). Leaf size: 73

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

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