45.2.12 problem 12

Internal problem ID [7235]
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
Date solved : Monday, January 27, 2025 at 02:48:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

Solution by Maple

Time used: 0.007 (sec). Leaf size: 52

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

Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 55

AsymptoticDSolveValue[x*D[y[x],{x,2}]+(x+3)*D[y[x],x]+7*x^2*y[x]==0,y[x],{x,0,"6"-1}]
 
\[ y(x)\to c_2 \left (\frac {7 x^4}{120}-\frac {7 x^3}{15}+1\right )+c_1 \left (\frac {2 x^4-2 x^3+2 x^2-2 x+1}{x^2}-\log (x)\right ) \]