67.2.55 problem Problem 20(b)

Internal problem ID [14012]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 20(b)
Date solved : Tuesday, January 28, 2025 at 06:12:33 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime }&=\left (25-6 x \right ) y \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 128

dsolve((2*x+x^2)*diff(y(x),x$2)+ (10+x+x^2)*diff(y(x),x)=(25-6*x)*y(x),y(x), singsol=all)
 

\[ y = \frac {-88447 x^{4} c_{2} {\mathrm e}^{-x -2} \left (x +2\right )^{7} \operatorname {Ei}_{1}\left (-x -2\right )+11970 x^{4} c_{2} {\mathrm e}^{-x} \left (x +2\right )^{7} \operatorname {Ei}_{1}\left (-x \right )+x^{4} c_{1} \left (x +2\right )^{7} {\mathrm e}^{-x}-76477 c_{2} x^{10}-970261 c_{2} x^{9}-5171184 c_{2} x^{8}-14871174 c_{2} x^{7}-24496796 c_{2} x^{6}-22249488 c_{2} x^{5}-9184784 c_{2} x^{4}-488880 c_{2} x^{3}+131040 c_{2} x^{2}-60480 c_{2} x +40320 c_{2}}{x^{4}} \]

✓ Solution by Mathematica

Time used: 0.318 (sec). Leaf size: 114

DSolve[(2*x+x^2)*D[y[x],{x,2}]+ (10+x+x^2)*D[y[x],x]==(25-6*x)*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x\left (\frac {4}{K[1]+2}-\frac {1}{2}+\frac {5}{2 K[1]}\right )dK[1]-\frac {1}{2} \int _1^x\left (-\frac {6}{K[2]+2}+1+\frac {5}{K[2]}\right )dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {-K[1]^2+11 K[1]+10}{2 K[1]^2+4 K[1]}dK[1]\right )dK[3]+c_1\right ) \]