Internal problem ID [70]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.5. Linear first order equations. Page 56
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y+\left (x +1\right ) y^{\prime }-\cos \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve([y(x)+(1+x)*diff(y(x),x) = cos(x),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\sin \relax (x )+1}{x +1} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 15
DSolve[{y[x]+(1+x)*y'[x] == Cos[x],y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sin (x)+1}{x+1} \\ \end{align*}