Internal problem ID [12334]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-\frac {y}{x}=\cos \left (x \right )} \] With initial conditions \begin {align*} [y \left (-1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(y(x),x)=y(x)/x+cos(x),y(-1) = 0],y(x), singsol=all)
\[ y \left (x \right ) = -\left (i \pi +\operatorname {Ci}\left (1\right )-\operatorname {Ci}\left (x \right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 14
DSolve[{y'[x]==y[x]/x+Cos[x],{y[-1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x (\operatorname {CosIntegral}(x)-\operatorname {CosIntegral}(-1)) \]