29.1.2 problem 1

Internal problem ID [4609]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 1
Date solved : Monday, January 27, 2025 at 09:26:10 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=x +\sin \left (x \right )+y \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(x),x) = x+sin(x)+y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = -x -1-\frac {\cos \left (x \right )}{2}-\frac {\sin \left (x \right )}{2}+{\mathrm e}^{x} c_{1} \]

✓ Solution by Mathematica

Time used: 0.071 (sec). Leaf size: 28

DSolve[D[y[x],x]==x+Sin[x]+y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x-\frac {\sin (x)}{2}-\frac {\cos (x)}{2}+c_1 e^x-1 \]