Internal problem ID [4549]
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]]
Solve \begin {gather*} \boxed {y^{\prime }+y-\left (1+x \right )^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 15
dsolve([diff(y(x),x)+y(x)=(x+1)^2,y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = x^{2}+1-{\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 16
DSolve[{y'[x]+y[x]==(x+1)^2,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2+\sinh (x)-\cosh (x)+1 \\ \end{align*}