40.16.4 problem 11

Internal problem ID [6795]
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
Date solved : Monday, January 27, 2025 at 02:30:41 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=2 x^{2}+3 y \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 52

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

\[ y = \left (1+3 x +\frac {9}{2} x^{2}+\frac {9}{2} x^{3}+\frac {27}{8} x^{4}+\frac {81}{40} x^{5}\right ) y \left (0\right )+\frac {2 x^{3}}{3}+\frac {x^{4}}{2}+\frac {3 x^{5}}{10}+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 61

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

\[ y(x)\to \frac {3 x^5}{10}+\frac {x^4}{2}+\frac {2 x^3}{3}+c_1 \left (\frac {81 x^5}{40}+\frac {27 x^4}{8}+\frac {9 x^3}{2}+\frac {9 x^2}{2}+3 x+1\right ) \]