Internal problem ID [2756]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 1
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-x -\sin \relax (x )-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 21
dsolve(diff(y(x),x) = x+sin(x)+y(x),y(x), singsol=all)
\[ y \relax (x ) = -x -1-\frac {\cos \relax (x )}{2}-\frac {\sin \relax (x )}{2}+c_{1} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 28
DSolve[y'[x]==x+Sin[x]+y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x-\frac {\sin (x)}{2}-\frac {\cos (x)}{2}+c_1 e^x-1 \\ \end{align*}