57.1.26 problem 26

Internal problem ID [9010]
Book : First order enumerated odes
Section : section 1
Problem number : 26
Date solved : Monday, January 27, 2025 at 05:27:11 PM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 24

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

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