Internal problem ID [11657]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }+3 x^{2} y=x^{2}} \] With initial conditions \begin {align*} [y \left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve([diff(y(x),x)+3*x^2*y(x)=x^2,y(0) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{3}+\frac {5 \,{\mathrm e}^{-x^{3}}}{3} \]
✓ Solution by Mathematica
Time used: 2.884 (sec). Leaf size: 20
DSolve[{y'[x]+3*x^2*y[x]==x^2,{y[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {5 e^{-x^3}}{3}+\frac {1}{3} \]