15.24.10 problem 10

Internal problem ID [3382]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 42, page 206
Problem number : 10
Date solved : Monday, January 27, 2025 at 07:35:19 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 47

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

\[ y \left (x \right ) = c_{1} x^{2} \left (1-x +\frac {9}{10} x^{2}-\frac {17}{30} x^{3}+\frac {251}{840} x^{4}-\frac {37}{280} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (12-12 x -18 x^{2}+44 x^{3}-\frac {115}{2} x^{4}+\frac {477}{10} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 64

AsymptoticDSolveValue[x^2*D[y[x],{x,2}]+2*x^2*D[y[x],x]-(3*x^2+2)*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (-\frac {115 x^3}{24}+\frac {11 x^2}{3}-\frac {3 x}{2}+\frac {1}{x}-1\right )+c_2 \left (\frac {251 x^6}{840}-\frac {17 x^5}{30}+\frac {9 x^4}{10}-x^3+x^2\right ) \]