Internal problem ID [2424]
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: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {3 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y=-x^{3}+x} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 63
Order:=6; dsolve(3*x^2*(x+1)*diff(y(x),x$2)+x*(5-x)*diff(y(x),x)+(2*x^2-1)*y(x)=x-x^3,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {c_{2} x^{\frac {4}{3}} \left (1+\frac {1}{7} x -\frac {1}{10} x^{2}+\frac {29}{2730} x^{3}-\frac {17}{87360} x^{4}-\frac {1193}{8299200} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+x^{2} \left (\frac {1}{4}+\frac {1}{60} x -\frac {47}{960} x^{2}+\frac {673}{52800} x^{3}-\frac {1169}{316800} x^{4}+\operatorname {O}\left (x^{5}\right )\right )+c_{1} \left (1+7 x -\frac {1}{2} x^{2}-\frac {29}{30} x^{3}+\frac {73}{480} x^{4}-\frac {167}{26400} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 255
AsymptoticDSolveValue[3*x^2*(x+1)*y''[x]+x*(5-x)*y'[x]+(2*x^2-1)*y[x]==x-x^3,y[x],{x,0,5}]
\[ y(x)\to \frac {c_1 \left (-\frac {167 x^5}{26400}+\frac {73 x^4}{480}-\frac {29 x^3}{30}-\frac {x^2}{2}+7 x+1\right )}{x}+c_2 \sqrt [3]{x} \left (-\frac {1193 x^5}{8299200}-\frac {17 x^4}{87360}+\frac {29 x^3}{2730}-\frac {x^2}{10}+\frac {x}{7}+1\right )+\sqrt [3]{x} \left (-\frac {1193 x^5}{8299200}-\frac {17 x^4}{87360}+\frac {29 x^3}{2730}-\frac {x^2}{10}+\frac {x}{7}+1\right ) \left (\frac {19491 x^{17/3}}{8800}-\frac {541 x^{14/3}}{256}+\frac {107 x^{11/3}}{55}-\frac {99 x^{8/3}}{64}+\frac {3 x^{5/3}}{5}+\frac {3 x^{2/3}}{8}\right )+\frac {\left (-\frac {167 x^5}{26400}+\frac {73 x^4}{480}-\frac {29 x^3}{30}-\frac {x^2}{2}+7 x+1\right ) \left (-\frac {652399 x^6}{2096640}+\frac {2039 x^5}{6825}-\frac {313 x^4}{1120}+\frac {5 x^3}{21}-\frac {x^2}{8}\right )}{x} \]