32.5.12 problem Exercise 11.11, page 97

Internal problem ID [5850]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli Equations
Problem number : Exercise 11.11, page 97
Date solved : Monday, January 27, 2025 at 01:20:44 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+2 y&=\sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(diff(y(x),x)+2*y(x)=sin(x),y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {\cos \left (x \right )}{5}+\frac {2 \sin \left (x \right )}{5}+{\mathrm e}^{-2 x} c_{1} \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 26

DSolve[D[y[x],x]+2*y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 \sin (x)}{5}-\frac {\cos (x)}{5}+c_1 e^{-2 x} \]