Internal problem ID [11576]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number: 3(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+3 y=3 x^{2} {\mathrm e}^{-3 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(x),x)+3*y(x)=3*x^2*exp(-3*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (x^{3}+c_{1} \right ) {\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.098 (sec). Leaf size: 17
DSolve[y'[x]+3*y[x]==3*x^2*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} \left (x^3+c_1\right ) \]