Internal problem ID [2400]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 41, page 195
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 x y^{\prime }-y \left (x +1\right )=0} \] With the expansion point for the power series method at \(x = 0\).
✗ Solution by Maple
Order:=6; dsolve(x^3*(3+x^2)*diff(y(x),x$2)+5*x*diff(y(x),x)-(1+x)*y(x)=0,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 99
AsymptoticDSolveValue[x^3*(3+x^2)*y''[x]+5*x*y'[x]-(1+x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {18968303719 x^5}{1220703125000}-\frac {20383193 x^4}{1953125000}+\frac {26731 x^3}{3906250}+\frac {259 x^2}{31250}+\frac {37 x}{125}+1\right ) \sqrt [5]{x}+c_2 e^{\left .\frac {5}{3}\right /x} \left (\frac {869909160612721304 x^5}{27030487060546875}+\frac {46847788879262 x^4}{4805419921875}+\frac {15542572604 x^3}{4271484375}+\frac {2270672 x^2}{1265625}+\frac {1372 x}{1125}+1\right ) x^{9/5} \]