15.22.2 problem 2

Internal problem ID [3336]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 40, page 186
Problem number : 2
Date solved : Monday, January 27, 2025 at 07:34:28 AM
CAS classification : [_linear]

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

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 16

Order:=5; 
dsolve([diff(y(x),x)=x*y(x)-x^2,y(0) = 2],y(x),type='series',x=0);
 

\[ y \left (x \right ) = 2+x^{2}-\frac {1}{3} x^{3}+\frac {1}{4} x^{4}+\operatorname {O}\left (x^{5}\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 22

AsymptoticDSolveValue[{D[y[x],x]==x*y[x]-x^2,{y[0]==2}},y[x],{x,0,"5"-1}]
 

\[ y(x)\to \frac {x^4}{4}-\frac {x^3}{3}+x^2+2 \]