8.4.17 problem 17

Internal problem ID [720]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 17
Date solved : Monday, January 27, 2025 at 02:59:09 AM
CAS classification : [_linear]

\begin{align*} y+\left (1+x \right ) y^{\prime }&=\cos \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 14

dsolve([y(x)+(1+x)*diff(y(x),x) = cos(x),y(0) = 1],y(x), singsol=all)
 

\[ y = \frac {\sin \left (x \right )+1}{x +1} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 15

DSolve[{y[x]+(1+x)*D[y[x],x] == Cos[x],y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sin (x)+1}{x+1} \]