60.3.259 problem 1264

Internal problem ID [11269]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1264
Date solved : Monday, January 27, 2025 at 11:01:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+3 x +4\right ) y^{\prime \prime }+\left (x^{2}+x +1\right ) y^{\prime }-\left (2 x +3\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 19

dsolve((x^2+3*x+4)*diff(diff(y(x),x),x)+(x^2+x+1)*diff(y(x),x)-(2*x+3)*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{-x}+c_{2} \left (x^{2}+x +3\right ) \]

✓ Solution by Mathematica

Time used: 0.286 (sec). Leaf size: 121

DSolve[(-3 - 2*x)*y[x] + (1 + x + x^2)*D[y[x],x] + (4 + 3*x + x^2)*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x-\frac {K[1] (K[1]+5)+7}{2 K[1] (K[1]+3)+8}dK[1]-\frac {1}{2} \int _1^x\frac {K[2]^2+K[2]+1}{K[2] (K[2]+3)+4}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}-\frac {K[1]^2+5 K[1]+7}{2 K[1]^2+6 K[1]+8}dK[1]\right )dK[3]+c_1\right ) \]