60.3.316 problem 1322

Internal problem ID [11326]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1322
Date solved : Monday, January 27, 2025 at 11:13:18 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }+2 x \left (3 x +2\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 44

dsolve(x^2*(x+1)*diff(diff(y(x),x),x)+2*x*(3*x+2)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = c_{1} +\left (-4 \ln \left (x \right )+4 \ln \left (x +1\right )-\frac {12 x^{3}+6 x^{2}-2 x +1}{3 x^{3} \left (x +1\right )}\right ) c_{2} \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 45

DSolve[2*x*(2 + 3*x)*D[y[x],x] + x^2*(1 + x)*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\exp \left (\int _1^{K[2]}-\frac {6 K[1]+4}{K[1]^2+K[1]}dK[1]\right ) c_1dK[2]+c_2 \]