2.12 problem 12

Internal problem ID [4814]

Book: A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G. Zill. 9th edition. Brooks/Cole. CA, USA.
Section: Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.2 page 239
Problem number: 12.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

Solve \begin {gather*} \boxed {x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).

Solution by Maple

Time used: 0.093 (sec). Leaf size: 56

Order:=6; 
dsolve(x*diff(y(x),x$2)+(x+3)*diff(y(x),x)+7*x^2*y(x)=0,y(x),type='series',x=0);
 

\[ y \relax (x ) = \frac {c_{1} \left (1-\frac {7}{15} x^{3}+\frac {7}{120} x^{4}-\frac {1}{150} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) x^{2}+\ln \relax (x ) \left (2 x^{2}-\frac {14}{15} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2}+\left (-2+4 x -3 x^{2}+4 x^{3}-4 x^{4}+\frac {547}{225} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2}}{x^{2}} \]

Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 55

AsymptoticDSolveValue[x*y''[x]+(x+3)*y'[x]+7*x^2*y[x]==0,y[x],{x,0,5}]
 

\[ y(x)\to c_2 \left (\frac {7 x^4}{120}-\frac {7 x^3}{15}+1\right )+c_1 \left (\frac {2 x^4-2 x^3+2 x^2-2 x+1}{x^2}-\log (x)\right ) \]