Internal problem ID [2430]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 43, page 209
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y \left (x +1\right )=x \left (x^{2}+x +1\right )} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 63
Order:=6; dsolve(2*x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+(1+x)*y(x)=x*(1+x+x^2),y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {c_{1} \left (1-x +\frac {1}{6} x^{2}-\frac {1}{90} x^{3}+\frac {1}{2520} x^{4}-\frac {1}{113400} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x}+\frac {c_{2} \left (1-\frac {1}{3} x +\frac {1}{30} x^{2}-\frac {1}{630} x^{3}+\frac {1}{22680} x^{4}-\frac {1}{1247400} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{\sqrt {x}}+x \left (\frac {1}{6}+\frac {1}{18} x +\frac {17}{504} x^{2}-\frac {17}{22680} x^{3}+\frac {17}{1496880} x^{4}+\operatorname {O}\left (x^{5}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 237
AsymptoticDSolveValue[2*x^2*y''[x]+5*x*y'[x]+(1+x)*y[x]==x*(1+x+x^2),y[x],{x,0,5}]
\[ y(x)\to \frac {c_1 \left (-\frac {x^5}{113400}+\frac {x^4}{2520}-\frac {x^3}{90}+\frac {x^2}{6}-x+1\right )}{x}+\frac {c_2 \left (-\frac {x^5}{1247400}+\frac {x^4}{22680}-\frac {x^3}{630}+\frac {x^2}{30}-\frac {x}{3}+1\right )}{\sqrt {x}}+\frac {\left (-\frac {x^5}{1247400}+\frac {x^4}{22680}-\frac {x^3}{630}+\frac {x^2}{30}-\frac {x}{3}+1\right ) \left (\frac {131 x^{11/2}}{4620}-\frac {76 x^{9/2}}{405}+\frac {x^{7/2}}{21}+\frac {2 x^{3/2}}{3}\right )}{\sqrt {x}}+\frac {\left (-\frac {x^5}{113400}+\frac {x^4}{2520}-\frac {x^3}{90}+\frac {x^2}{6}-x+1\right ) \left (-\frac {103 x^6}{19440}+\frac {19 x^5}{315}-\frac {7 x^4}{40}-\frac {2 x^3}{9}-\frac {x^2}{2}\right )}{x} \]