Internal problem ID [14970]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 3. The method of successive approximation. Exercises page 31
Problem number: 43.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-y=x} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve([diff(y(x),x)=x+y(x),y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = -x -1+2 \,{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 15
DSolve[{y'[x]==x+y[x],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x+2 e^x-1 \]