Internal problem ID [14120]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Review exercises, page
23
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+2 y=x^{2}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve([diff(y(x),x)+2*y(x)=x^2,y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{2}}{2}-\frac {x}{2}+\frac {1}{4}+\frac {3 \,{\mathrm e}^{-2 x}}{4} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 26
DSolve[{y'[x]+2*y[x]==x^2,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (2 x^2-2 x+3 e^{-2 x}+1\right ) \]