2.55 problem Problem 20(b)

Internal problem ID [10928]

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)
 

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

✓ Solution by Mathematica

Time used: 0.332 (sec). Leaf size: 109

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

\begin{align*} y(x)\to \frac {e^{-x-2} \left (c_2 x^4 (x+2)^7 \left (11970 e^2 \operatorname {ExpIntegralEi}(x)-88447 \operatorname {ExpIntegralEi}(x+2)\right )+e^2 \left (322560 c_1 x^4 (x+2)^7+c_2 e^x (x (x (x (x (x (x (x (x (x (76477 x+970261)+5171184)[phone])[phone])[phone])+9184784)[phone])[phone])\right )\right )}{322560 x^4} \\ \end{align*}