Internal problem ID [11956]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime }-\left (25-6 x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 113
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)
\[ y \left (x \right ) = c_{1} \left (x +2\right )^{7} {\mathrm e}^{-x}+\frac {c_{2} \left (88447 \left (x +2\right )^{7} x^{4} {\mathrm e}^{-x -2} \operatorname {Ei}_{1}\left (-x -2\right )-11970 \,{\mathrm e}^{-x} x^{4} \left (x +2\right )^{7} \operatorname {Ei}_{1}\left (-x \right )+76477 x^{10}+970261 x^{9}+5171184 x^{8}+14871174 x^{7}+24496796 x^{6}+22249488 x^{5}+9184784 x^{4}+488880 x^{3}-131040 x^{2}+60480 x -40320\right )}{x^{4}} \]
✓ Solution by Mathematica
Time used: 1.158 (sec). Leaf size: 217
DSolve[(2*x+x^2)*y''[x]+ (10+x+x^2)*y'[x]==(25-6*x)*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-x-2} \left (11970 e^2 c_2 x^4 (x+2)^7 \operatorname {ExpIntegralEi}(x)-88447 c_2 x^4 (x+2)^7 \operatorname {ExpIntegralEi}(x+2)+e^2 \left (322560 c_1 x^{11}+x^{10} \left (76477 c_2 e^x+4515840 c_1\right )+x^9 \left (970261 c_2 e^x+27095040 c_1\right )+144 x^8 \left (35911 c_2 e^x+627200 c_1\right )+6 x^7 \left (2478529 c_2 e^x+30105600 c_1\right )+4 x^6 \left (6124199 c_2 e^x+54190080 c_1\right )+48 x^5 \left (463531 c_2 e^x+3010560 c_1\right )+112 x^4 \left (82007 c_2 e^x+368640 c_1\right )+488880 c_2 e^x x^3-131040 c_2 e^x x^2+60480 c_2 e^x x-40320 c_2 e^x\right )\right )}{322560 x^4} \]