Internal problem ID [5452]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 25. Integration in series. Supplemetary problems. Page 205
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-3 y=2 x^{2}} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
Order:=6; dsolve(diff(y(x),x)=2*x^2+3*y(x),y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1+3 x +\frac {9}{2} x^{2}+\frac {9}{2} x^{3}+\frac {27}{8} x^{4}+\frac {81}{40} x^{5}\right ) y \left (0\right )+\frac {2 x^{3}}{3}+\frac {x^{4}}{2}+\frac {3 x^{5}}{10}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 61
AsymptoticDSolveValue[y'[x]==2*x^2+3*y[x],y[x],{x,0,5}]
\[ y(x)\to \frac {3 x^5}{10}+\frac {x^4}{2}+\frac {2 x^3}{3}+c_1 \left (\frac {81 x^5}{40}+\frac {27 x^4}{8}+\frac {9 x^3}{2}+\frac {9 x^2}{2}+3 x+1\right ) \]