Internal problem ID [2365]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-y x=-x^{2}} \] With initial conditions \begin {align*} [y \left (0\right ) = 2] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (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: 0.003 (sec). Leaf size: 22
AsymptoticDSolveValue[{y'[x]==x*y[x]-x^2,{y[0]==2}},y[x],{x,0,4}]
\[ y(x)\to \frac {x^4}{4}-\frac {x^3}{3}+x^2+2 \]