Internal problem ID [5057]
Book: Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section: Chapter 10, Differential equations. Section 10.3, ODEs with variable Coefficients. First
order. page 315
Problem number: 10.3.4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y+y^{\prime }=\left (x +1\right )^{2}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve([diff(y(x),x)+y(x)=(x+1)^2,y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = x^{2}+1-{\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.102 (sec). Leaf size: 17
DSolve[{y'[x]+y[x]==(x+1)^2,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2-e^{-x}+1 \]